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(i)

T¦Uû] LQdÏ UtßmA±®Vp

(Workshop Calculation and Science)NSQF

ØRp TÚYm

(1st Semester)

Aû]jÕ ùTô±«Vp ©¬ÜLÞdÏm

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(COMMON FOR All ENGINEERING TRADES)

T«t£jÕû\ ùTôÕ CVdLLm,§\uªÏ úUmTôÓ Utßm ùRô¯p Øû]úYôo AûUfNLm,

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© NIMI, Not to be republished

(ii)

T¦Uû] LQdÏ Utßm A±®Vp (NSQF) ØRp TÚYm

Workshop Calculation and Science 1st Semester

Aû]jÕ ùTô±«Vp ©¬ÜLÞdÏm ùTôÕYô]Õ

Common for all Engineering Trades

T§l×¬ûU © 2019 úR£V ùRô¯t T«t£ FPL RVô¬l× ¨ûXVm, ùNuû].

ØRtT§l× : Uôof 2019 ©W§Ls : 1000

Rs. 160/-

E¬ûU : úR£V ùRô¯t T«t£ FPL RVô¬l× ¨ûXVm, ùNuû].

úR£V ùRô¯t T«t£ FPL RVô¬l× ¨ûXVm, ùNuû]«u AàU§ CpXôUp CkR ©WÑWj§u

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ApXÕ CVk§WêXm, úTôhúPô SLp, T§Ü ùNnRp ApXÕ RLYp úNªl× Utßm GkR

Y¯Øû\«Ûm §ÚmTl ùTßm YN§«û] ùNnVdáPôÕ.

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úR£V ùRô¯t T«t£ FPL RVô¬l× ¨ûXVm

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¡i¥, ùNuû] þ 600 032ùRôûXúT£ : 044þ2250 0248, 2250 0657, 2250 2421

ùRôûXSLp (Fax) : 91-44-2250 0791ªu AOóNp (Email) : [email protected], [email protected]

YûXR[m (Website) : www.nimi.gov.in


(iii)

ØuàûW

Ck§V AWNôeLj§u úTWôYp CXdLô], 30 úLô¥ UdLÞdÏ, SôpYôõp JÚYÚdÏúYûX Ej§WYôRjûR 2020 Bi¥tÏs HtTÓjR úR£V §\u úUmTôhÓ ùLôsûLHtTÓjRlThÓs[Õ. §\u ªÏ ûL®û]OôóLû[ EÚYôdÏY§p ùRô¯t T«t£¨ûXVeLs (ITI) Ød¡V TeÏ YÏd¡\Õ. CdÏ±dúLô°u A¥lTûP«p RtLôXùRô¯tNôûXL°u úRûYdúLtT §\uªÏ ûL®û]OôóLû[ EÚYôd¡T«t£V°lTRtLôL ùRô¯tT«t£ TôP§hPj§û] (ITI syllabus) Uôt±VûUdL,ùRô¯tLp® T«tß]ôóLs, Lp®Vô[oLs Utßm TpúYß ©W§¨§Lû[ Es[Pd¡VJÚ ÏÝYô]Õ EÚYôdLlThPÕ. AdÏÝ®u TeÏRôWoL[ôL ùRô¯tNôûXL°p T¦×¬úYôo, ùRô¯p Øû]úYôo, Lp®Vô[oLs Utßm (ITI) -u ©W§¨§Ls APeÏYo.

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CWôú_x ALoYôp, I. A. S.,ùTôÕ CVdÏSo / CûQ ùNVXô[o

§\u úUmTôÓ Utßm ùRô¯p

Øû]úYôôó AûUfNLm

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×Õ ¥p≠ þ 110 001.


(iv)

ØLÜûW

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CkR Lt©jRÛdLô] NôR]eLs JÚ LÚj§Vp FPL £lTeLs Y¥®p (IMP) LÚj§Vp ×jRLm,ùNnØû\ ×jRLm, úNôRû] Utßm §\]ônÜ T«t£ (Test & Assignment) ×jRLm, T«tßSôóY¯Lôh¥, úLh£ Lôh£ LÚ® (ÑYôó ®[dLlTPm Utßm Jüõ×Ïm FPLm) B¡VYtû\Es[Pd¡«ÚdÏm. CkR NôR]eLs ùRô¯tT«t£ ¨ûXVj§u (ITI) T«t£«u JhÓ ùUôjRRWj§û] EVojR TVuTÓm.

“§\u Ck§Vô” Guß AûZdLlTÓ¡\ úR£V Tp§\u (multi skill) §hPØuYûWÜ (programes),Ck§V AW£u ̈ § AûUfNLj§u (ùTôÚ[ôRôW ©¬Ü)þu ̧ r 27þ12þ2013 úR§«hP AWNôûQ«uYô«XôL ùY°«PlThPÕ. CRu êXm §\u úUmTôh¥u ¸r Ck§V Cû[OoLÞdÏ A±ÜUtßm §\ûUûV A§L¬dL Y¯YûL ùNnÕ ARu êXm ×§V Yônl×Lû[ EÚYôdLÜm§hPªPlThPÕ.

CRu Ød¡VjÕYm Ck§V Cû[OoL°u §\û] úUmTÓj§ ARuêXm AYoLs úYûXYônl× ùT\Üm, úUÛm ùRô¯p Øû]úYôo T«t£ A°jRp êXm, AYoLs ÑV ùRô¯p ×¬VBRWÜ Utßm Y¯LôhÓRp êXm Sm TôWmT¬V ùRô¯ûXÙm £\lTôL ùNnV Ø¥Ùm. CkRT«t£Ls NoYúRN RWj§u A¥lTûP«p CÚlTRôp, Sm Sôh¥u Cû[OoLs Ck§VA[®ÛmUtßm AVpSôh¥Ûm T¦×¬VÜm Y¯ YûL HtTÓm. CkR “úR£V §\u RÏ§LhPûUl×” (NSQF) úR£V §\u úUmTôhÓ ØLûU (NSDA) Guß AûZdLlTÓ¡\AûUl©]Wôp C§p GpXô®RUô] RÏ§Lû[Ùm JÚ ùRôPof£Vô] A±Ü ¨ûX, §\u,GiQm úUmTôÓ B¡VYtû\ AûPV Ø¥Ùm. CkR NSQF þu ¸r T«t£Vô[o GkR¨ûXdLô]RÏ§ ¨ûXûVÙm úSW¥ T«t£ êXúUô ApXÕ Uû\ØL T«t£ êXúUô ApXÕ AàTYT«t£«u êXUôLúYô AûPV Ø¥Ùm.

CkR T¦Uû] LQdÏ Utßm A±®Vp (Aû]jÕ ùTô±«Vp ©¬ÜLÞdÏm ùTôÕYô]Õ)×jRLUô]Õ Ød¡V ÏÝ Eßl©]oL[ôp NSQF TôPj§hPj§u ¸r EÚYôdLlThPÕ.

CkR T¦Uû] LQdÏ Utßm A±®Vp NSQF TôPj§hPj§u T¥ (Aû]jÕ ùTô±«Vp©¬ÜLÞdÏm ùTôÕYô]Õ) ØRp TÚY ×jRLm Ød¡V ÏÝ Eßl©]oL°u áhÓ ØVt£VôÛm(C§p Lp®Vô[o/ ùRô¯p Øû\ Lp® ¨ßY]eL[ô] (IIT) Utßm TX) Utßm (DGE&T) þu ¸rCVeÏm ùRô¯t T«t£ ¨ûXVeL°p T¦ ×¬Ùm AYWYo ùRô¯p Õû\«p §\]ôLEs[YoLs, Utßm (MDC) Eßl©]oLs Utßm (NIMI) F¯VoLs B¡úVôoL[ôpEÚYôdLlThPRôÏm. úUúX á\lThP ×jRLm, T«tß®lTYo Utßm T«t£Vô[¬u ¿iPSôû[V ®ÚlTUô] ùRô¯p NôokR Õû\«p T«t£ ùLôÓjÕ úYûX Yônl©û] A§L¬dÏm®RUôL ØÝûUVôL §Úl§ A°dÏm G] Sm©dûL ùR¬®jÕ (NIMI) YôrjÕ¡\Õ.

CfNkRolTj§p (NIMI), GpXô Eßl©]oLÞdÏm Utßm FPL RVô¬l× ÏÝ Eßl©]oLÞdÏmR]Õ EiûUVô] Su±«û] ùR¬®jÕd ùLôs¡\Õ.

Bo. ©. §eWôùNuû] - 600 032 ùNVp CVdÏSo, NIMI


(v)

HtT±®l×

NSQF TôPj§hPj§uT¥ (ØRp TÚYm) “T¦Uû] LQdÏ Utßm A±®Vp” (Aû]jÕùTô±«Vp ©¬ÜLÞdÏm ùTôÕYô]Õ) ùRô¯tT«t£ FPL £lTeLû[ (IMP)ùY°dùLôQW LôWQUô] ¸rLiP FPL RVô¬l× Eßl©]oL°u JjÕûZl× Utßm

AYoL°u TeL°l©tÏ úR£V ùRô¯tT«t£ FPL RVô¬l× ¨ûXVm (NIMI) R]Õ

Su±«û] ùR¬®jÕd ùLôs¡\Õ.

FPL úUmTôh¥u JÚe¡ûQlTô[oLs

§Ú. K. º²YôN Wôq - CûQ CVdÏSo,

UiPX ùUô¯ ùTVol× ùTôßlTô[o,

NIMI, ùNuû].

§Ú. G . ûUd¡s _ô² - T«t£ AÛYXo,

JÚe¡ûQlTô[o NIMI,ùNuû].

RªZôdLm

§Ú. C.C . Ñl©WU¦Vu - T«t£ A§Lô¬, (KnÜ)

TôX Uk§o PHMITI,ùNuû] þ 600017

§Ú. G . ù_VWôUu - ER® T«t£ AÛYXo, (KnÜ)

AW£]o ùRô¯tT«t£ ¨ûXVm,

AmTjço, ùNuû] þ 600058

CkR £lTjûR (IMP) EÚYôdÏm ùNVtTôh¥p ªLÜm £\lTôLÜm BrkR DÓTôÓPàmT¦Vôt±V L¦² RhPfNo, L¦² YûW LûXOo ªûN AfÑl T§lTô[o B¡úVôÚdÏ

úR£V ùRô¯tT«t£ FPL RVôôõl× ¨ûXVm (NIMI) R]Õ TôWôhÓRûXl T§Ü ùNn¡\Õ.

CkR ×jRLjûR EÚYôdLl TeL°l× Sp¡V CRW T¦Vô[oL°u ØVt£LÞdÏm úR£V

ùRô¯tT«t£ FPL RVôôõl× ¨ûXVm (NIMI) R]Õ Su±ûVj ùR¬®jÕd ùLôs¡\Õ.


(vi)

A±ØLm

Cl×jRLm ÑVUôL LtTRtÏ Ht\ AXÏL[ôL ©ôõdLlThÓs[Õ. JqùYôÚ RûXl©tÏm Ht\ûRÑÚdLUôL §Wh¥ ùLôÓdLlThÓs[Õ Utßm §\]ônÜ T«t£ TÏ§Ùm Es[Pe¡VÕ.ùR°YôLÜm, ÑXTUôLÜm ×ôõkÕùLôs[dá¥V Øû\«p T¦Uû] LQdÏLs Utßm A±®VpA¥lTûP RjÕYeLs ÑÚdLUôL ®YôõdLlThÓs[Õ. YÏl× Aû\«p T«t£Vô[oLÞdÏT«tß]ôó A°dÏm ®[dL EûWdÏ CûR JÚ Uôt\ôLd LÚRdáPôÕ. ¨fNVUôL CÕ ªLÜm®ôõYô]RôL CÚdÏm. Cl×jRLj§u êXm T«t£Vô[oLs úRûYVô]ûYLû[ ùT\ Ø¥Ùm.T«tß]o êXm ®ôõYôL ùRôõkÕ ùLôs[Xôm Utßm AkRkR TÏ§«p Es[ §\]ônÜT«t£Lû[ ÑVUôL ¾oÜ LôQXôm. TXYûLVô] LQdÏLû[ Cl×jRLj§u ER®Vôp ¾oÜLôQXôm. T¦Uû]«p ùNnØû\ T«t£«u ùTôÝÕ HtTPdá¥V NkúRLeLÞdÏ CÕ ªLÜmER®VôL CÚdÏm.

§\]ônÜ T«t£, YûWLûX (graphics) êXUôL ùLôÓdLlThÓs[Rôp T«t£Vô[o G°RôL×¬kÕ ùLôs[ Ø¥Ùm. úUÛm LQdÏLû[ ¾oÜ LôiTRtÏ N¬Vô] Y¯Øû\Lû[ CRuêXm T«t£Vô[oA±VXôm. LQdÏLû[ ¾oÜ ùNnYRtÏj úRûYVô] Ï±l×Ls (data)YûWLûXdÏ AÚ¡p Ï±ÂÓLs (A) YôojûRLs êXm ùLôÓdLlThÓs[Õ. LQdÏL°pÏ±dLlThP Ï±ÂÓLs HtL]úY ARtÏj ùRôPo×ûPV RûXl×f ÑÚdLj§p Es[Õ

JqùYôÚ T«t£«u Ø¥®Ûm GeÏ úRûYúVô AeÏ ARtÏj úRûYVô] §\]ônÜ T«t£Ls,

LQdÏLs úUÛm T«t£dLôL ùLôÓdLlThÓs[].

JÕdLlThP úSWm:

ØRp TÚYj§tLô] LôX AYLôNm (26 YôWeLs) : 52 U¦ úSWm

¡ûPdLlùTt\ TVàs[ YôWeLs (22 YôWeLs) : 44 U¦ úSWm

§Úl×Rp Utßm úRoÜLs (4 YôWeLs) : 8 U¦ úSWm

JÕdLlThP ùUôjR úSWm : 52 U¦ úSWm

JqùYôÚ TÏ§dÏm JÕdLlThP LôX A[ÜLs ¸úZ ùLôÓdLlThÓs[]. T«tß]oLs CkRLôX AYLôNj§û] TVuTÓj§d ùLôsÞUôß úLhÓd ùLôs[lTÓ¡\ôoLs.

Y.Gi TÏ§ T«t£ Gi JÕdLlThP úSWm (U¦«p)

1 AXÏ Øû\Ls, LôW¦Ls Utßm 1.1.01 - 1.2.09 10 U¦ úSWm©u]eLs

2 YodL êXm, ®¡Rm Utßm ®¡R 1.3.10 - 1.5.16 12 U¦ úSWmNUm, NRÅRm

3 CVtL¦Rm (ØRp TÚY EúXôLj 1.6.17 - 1.6.18 4 U¦ úSWmRLÓ úYûXVôs (SMW) -dÏ UhÓm)

4 ùTôÚs A±®Vp, ¨û\, GûP 1.7.19 - 1.8.26 14 U¦ úSWmUtßm APoj§

5 úYLm Ut\m §ûN úYLm, úYûX, 1.9.27 - 1.10.30 8 U¦ úSWm§\u Utßm Bt\p

6 ùYlTm Utßm ùYlT¨ûX (ØRp TÚY 1.11.31 - 1.12.37 6 U¦ úSWmMR&AC Utßm EúXôLjRLÓ úYûXVôs(SMW) -dÏ UhÓm)

7 A¥lTûP ªu²Vp (ØRp TÚY 1.13.38 - 1.13.41 9 U¦ úSWmMR&AC -dÏ UhÓm)


(vii)

ùTôÚ[PdLm

T«t£ Gi T«t£L°u RûXl×Ls TdL Gi

TÏ§ 1

1.1.01 AXÏØû\L°u YûLLs (Classification of system of units) 1

1.1.02 A¥lTûP Utßm YûWVßdLlThP AXÏLs F.P.S,C.G.S, M.K.S Utßm SI AXÏLs (Fundamental and Derived unitsF.P.S, C.G.S, M.K.S and SI units) 3

1.1.03 A[ÅhÓ AXÏLs Utßm Uôt\eLs (Measurement unitsand conversion) 6

1.1.04 ¿[m, ¨û\, ®ûN, úYûX, §\u Utßm Bt\ûXUôtßRp (Conversions of length, mass, force,work, power and energy) 14

1.2.05 LôW¦Ls, HCF, LCM Utßm LQdÏLs (Factors, HCF,LCM and problems) 16

1.2.06 ©u]eLs (Fractions) 18

1.2.07 RNU ©u]eLs (Decimal fractions) 21

1.2.08 TôdùLh LôpÏúXhPo Utßm ARu TVuTôÓLs (Pocketcalculator and its applications) 25

1.2.09 LôpÏúXhPûW TVuTÓj§ ¾oÜ LôÔRp (Solving problemsby using calculator) 29

TÏ§ 2

1.3.10 YodLm Utßm YodLêXm (Square and square root) 32

1.3.11 LôpÏúXhPûW TVuTÓj§ G°V LQdÏLs ùNnRp(Simple problems using calculator) 33

1.3.12 ©RôLWv úRt\jûR TVuTÓj§ ùNnVlThPLQdÏLs (Applications of pythagoras theorem and related problems) 34

1.4.13 ®¡Rm Utßm ®¡R NUm (Ratio and proportion) 35

1.4.14 úSôó Uô\p Utßm G§ôó Uô\p (Direct and indirect proportions) 37

1.5.15 NRÅRm (Percentage) 42

1.5.16 NRÅRj§≠ÚkÕ RNU©u]m Utßm NôRôWQ ©u]UôLUôtßRp (Changing percentage to decimal and fraction) 46

TÏ§ 3 (ØRp TÚY EúXôLjRLÓ úYûXVôs(SMW) -dÏ UhÓm)

1.6.17 CVtL¦Rd Ï±ÂÓLs Utßm A¥lTûPLs(Algebraic symbols and fundamentals) 47

1.6.18 CVtL¦Rj§p Es[ ©¬Yô] áhPp, L¯jRp, ùTÚdLpUtßm YÏjRp (Addition,subtraction,multiplication and divisionof algebra) 51

TÏ§ 4

1.7.19 EúXôLeL°u CVt©Vp Utßm CVk§W®Vp RuûULs(Physical and mechanical properties of metals) 54


(viii)


1.7.20 CÚm× Utßm Yôol× CÚm©tLô] A±ØLm (Introduction ofiron and cast iron) 57

1.7.21 CÚm×fNjÕs[ Utßm CÚm×fNj§pXôR EúXôLYûLLs (Types of ferrous and non ferrous metals) 61

1.7.22 CÚm©tÏm, G@¡tÏm CûPúVVô] ®j§VôNeLs, LXl×G@Ï Utßm LôoTu G@Ï (Difference between iron & steel, alloysteel & carbon steel) 65

1.7.23 CWlTo, UWm Utßm CuÑúXh¥e ùTôÚsLÞdLô]RuûULs Utßm ETúVôLeLs (Properties and uses of rubber,timber and insulating materials) 67

1.8.24 ¨û\, ¨û\«u AXÏLs, APoj§ Utßm GûP (Mass,units of mass, density and weight) 71

1.8.25 ¨û\ Utßm GûPdÏ CûPúVVô] ®j§VôNm, APoj§Utßm APoj§ GiÔdÏ CûPúVVô] ®j§VôNm(Difference between mass & weight, density & specific gravity) 72

1.8.26 ¨û\, GûP Utßm APoj§ B¡VYtßdLô] ùRôPo×LQdÏLÞm §\]ônÜ T«t£LÞm (Related problems withassignment of mass, weight & density) 74

TÏ§ 5

1.9.27 KnÜ, CVdLm, úYLm, §ûN úYLm, úYLm Utßm §ûNúYLj§tLô] úYßTôÓ, ØÓdLm Utßm Ïû\ØÓdLm(Rest, motion, speed, velocity, difference between speed & velocity,acceleration & retardation) 81

1.9.28 úYLm Utßm §ûNúYLj§tÏ ùRôPo×ûPVLQdÏLÞm §\]ônÜ T«t£LÞm (Related problems withassignment of speed & velocity) 87

1.10.29 úYûX«u AXÏ, §\u Utßm Bt\p, Cu_÷²uÏ§ûWj§\u Utßm CVk§W XôTm (Units of work, power andenergy, horse power of engines and mechanical efficiency) 91

1.10.30 ¨ûX Bt\p, CVdL Bt\p Utßm AYt±tÏùRôPo×ûPV LQdÏLs Utßm §\]ônÜ T«t£ (Potentialenergy, kinetic energy and related problems with assignment ) 94

TÏ§ 6 (ØRp TÚY MR&AC Utßm EúXôLjRLÓúYûXVôs (SMW) -dÏ UhÓm)

1.11.31 ùYlTm Utßm ùYlT¨ûX LÚjÕÚ, ùYlTj§u®û[ÜLs, ùRoúUôÁhPo vúLp, ùNp£Vv, @TôWuaöh, ìUo, ùLp®u Utßm ùYlTm Utßm ùYlT¨ûXdÏCûPúVVô] úYßTôÓLs (Concept of heat and temperature,effects of heat, thermometer scale, celcius, fahrenheit, reaumer, kelvin anddifference between heat and temperature) 97

1.11.32 ùYlT¨ûXLû[ ùNu¥¡úWÓ, @TôWu aöh, ìUo,ùLp®u B¡V vúLpL°p Uôt\m ùNnRp (Conversionbetween centigrade, fahrenheit, reaumer, kelvin scale of temperature) 100


(ix)


1.11.33 ùYlT¨ûXûV A[dÏm LÚ®Ls, ùYlTUô²«uYûLLLs, ûTúWôÁhPo Utßm ùYlT T¬Uôt\m(Temperature measuring instruments, types of thermometer, pyrometerand transmission of heat ) 101

1.11.34 ¿[l ùTÚdL Gi Utßm ARtÏ ùRôPo×ûPVLQdÏLs Utßm §\]ônÜ T«t£ (Co-efficient of linearexpansion and related problems with assignment) 104

1.11.35 ùYlT CZl× Utßm ùYlT Ht× LQdÏLs Utßm§\]ônÜ T«t£ (Problems of heat loss and heat gain with assignment) 107

1.11.36 AÝjRj§u LÚjÕÚ Utßm TpúYß Øû\L°p ARuAXÏLs (Concept of pressure and its units in different system ) 112

1.12.37 ùYlT LPjÕm §\u Utßm Lôl× ùTôÚsLs (Thermalconductivity and insulations) 113

TÏ§ 7 (ØRp TÚY MR&AC -dÏ UhÓm)

1.13.38 A±ØLm, ªuNôWj§u ETúVôLeLs, Uô≠dëp,AÔ, ªuNôWm RVô¬jRp, ªuú]ôhPm, ªu]ÝjRm,ªuRûP Utßm ARu AXÏLs (Introduction, use of electricity,molecule, atom, producing electricity, electric current, voltage, resistanceand their units ) 116

1.13.39 Kªu ®§, LQdÏLs Utßm V.I.R CûP«Xô] E\ÜLs,ùRôPo ªu ÑtßLs Utßm CûQªu ÑtßL°uLQdÏLs (Ohm’s law, relation between V.I.R & problems, series & parallelcircuits problem ) 118

1.13.40 ªuNd§, Bt\p Utßm ARu AXÏLs, §\]ônÜ T«t£Utßm LQdÏLs (Electrical power, energy and their units, calculationwith assignment ) 121

1.13.41 LôkR çiPp, Ru ªu çiPp Utßm TWvTW ªuçiÓ§\u Utßm ªu CVdÏ ®ûN EtTj§ (Magneticinduction, self and mutual inductance and EMF generation ) 127

Lt\≠u ØÝûUûV U§lÀÓ ùNnÙm Øû\ LEARNING / ASSESSABLE OUTCOME

Cl×jRLj§u Ø¥®p ¿eLs §\m ùT\ CÚlTûY

• A¥lTûP ªu²Vp ARu Au\ôP TVuTôÓ, CûRl Tt±VTôPl×¬RÛPu TpúYß YûLVô] L¦Rm Utßm A±®VpTVuTôÓLs Utßm AYtû\ G°ûUVôL ×¬kÕ ùLôsÞRp[TpúYß YûL L¦Rm Utßm A±®Vp - AXÏLs, LôW¦Ls-Utßm ©u]eLs, YodL êXm, ®¡Rm Utßm ®¡R NUm,NRÅRm, ùTôÚs A±®Vp, ¨û\, GûP, APoj§, úYLmUtßm §ûNúYLm, úYûX, §\u Utßm Bt\p, CVtL¦Rm,ùYlTm Utßm ùYlT¨ûX, ªuNôWj§u A¥lTûP, AÝjRm]

• SMW - CVtL¦Rm Utßm ùYlTm Utßm ùYlT¨ûX

• MR & AC - ùYlTm Utßm ùYlT¨ûX Utßm ªuNôWj§uA¥lTûP


(x)

SYLLABUSFirst Semester Common for All Engineering Trades Duration: Six Months

(Except MR&AC and SMW)

S.no. Title

Unit

Fractions

Square Root

Square and Square Root, method of finding out square roots, Simple problem using calculator.

Ratio & Proportion

Simple calculation on related problems.

Introduction, Simple calculation. Changing percentage to decimal and fraction and vice-versa.

Percentage

Fractions, Decimal fraction, L.C.M., H.C.F., Multiplication and Division of Fractions and Decimals,conversion of Fraction to Decimal and vice versa. Simple problems using Scientific Calculator.

1

2

3

4

5

Systems of unit- FPS, CGS, MKS/SI unit, unit of Length, Mass and Time, Conversion of units.

Material Science

Properties - Physical & Mechanical, Types - Ferrous & Non-Ferrous, difference between Ferrous andNon-Ferrous metals, introduction of Iron, Cast Iron, Wrought Iron, Steel, difference between Iron andSteel, Alloy steel, Carbon steel, Stainless steel, Non-Ferrous metals, Non-Ferrous Alloys.

6

Mass, Weight and Density

Mass, Unit of Mass, Weight, difference between mass and weight, Density, unit of density, SpecificGravity of metals.

7

Speed and Velocity

Rest and Motion, Speed, Velocity, difference between speed and velocity, Acceleration, Retardation,equations of motions, simple related problems.

8

Work, Power and Energy

Work, unit of work, Power, unit of power, Horse power of engines, Mechanical Efficiency, Energy,use of energy, Potential and Kinetic energy, examples of potential energy and kinetic energy.

9


(xi)

Mechanic Refrigeration and Air Conditioning

General simplifications

Fractions, Types of fractions, Common fractions, Decimal fractions with examples. Addition,Subtraction, Multiplication and Division of fraction, conversion of Fraction to Decimal and vice versa.

S.no. Title

1

2 Square & Square root

Square root of perfect square, Square of Whole Number and Decimal. Applications of Pythagorastheorem and related Problems.

3 Unit & Measurements

Definition, classification of System of units, Fundamental & Derived units. C.G.S, M.K.S,. F.P.S, & S.ISystem of units. Metric system of weight and measurement unit and conversion factors, problems.

4 Percentage

Introduction, Simple calculation. Changing percentage to fraction and decimal & vice-versa.

5 Introduction, use of Electricity, Molecule, Atom, and How Electricity is Produced, Electric current,Voltage, Resistance and their units. Ohm’s law. Relation between V.I.R & Problems. Series & Parallelcircuits & Problems. Electrical Power and energy & their units & calculation.

6 Magnetic Induction, Self & Mutual Inductance, EMF generation.

7 Material Science

Properties of metals - Physical & Mechanical, Meaning of Tenacity, Elasticity, Malleability, Brittleness,Hardness, Ductility. Types – Ferrous & Non-Ferrous, difference between Ferrous and Non-Ferrousmetals, introduction of Iron, Cast Iron, Wrought Iron, Steel, difference between Iron and Steel, Alloysteel, Carbon steel, Stainless steel, Non-Ferrous Alloys. Effect of Alloying elements.

8 Properties and uses of Copper, Zinc, Lead, Tin, Aluminium etc., Properties and uses of Brass,Bronze as bearing material.

9 Heat and Temperature

Measurement of Temperature, Boiling and Melting points. Interchange of heat, (Principle ofcalorimetry) Co-efficient of linear expansion, Related problems.

10 Vapours and gases

Saturated and superheated vapours, Critical pressures and temperatures. Heat transfer -Conduction, Convection, Radiation. Thermal conductivity and Insulations.

Syllabus for Mechanic Refrigeration & Air Conditioning


(xii)

Sheet Metal Worker

Introduction and Importance of Science and Calculation to the Trade skill.

S.no. Title

1

2 - System of Units: British, Metric and S. I. Units for Length, Mass, Area, Volume, Capacity andTime.

- Conversions between British and Metric Systems.

3 - Density & Specific gravity.

- Mass, Weight. Definition and units.

4 - Metals: Properties and uses of Cast iron, Wrought iron, Plain carbon steels and Alloy steels.

- Difference between metals, non-metals and alloys.

5 Properties and uses of Copper, Zinc, Lead, Tin and Aluminium.

6 Properties and uses of Brass, Bronze, Rubber ,Timber and Insulating materials.

7 Concept of Heat and Temperature. Difference between heat and temperature. Effects of Heat,Thermometer Scales such as Celcius, Fahrenheit and Kelvin, Temperature measuring Instruments -types of thermometers and pyrometers.

8 - Conversions between the above Scales of Temperature.

- Units of Heat-Calorie, B.Th.U & C.H.U., Joule.

- Concept of Specific Heat, Latent Heat, problems on Heat Loss and Heat Gain.

9 - Definition of Force: Units of Force in M.K.S.& S.I. Systems.

- Concept of Pressure and its Units in different systems.

10 - General simplifications: BODMAS rule.

- Fraction: Addition, Subtraction, Multiplication and Division-Problems.

- Decimal: Addition, Subtraction, Multiplication, and Division-Problems.

11 Conversion of Fraction to Decimal and vice-versa.

12 Square roots: The Square and Square root of a Whole Number and Decimal.

13 Percentage: Changing Percent to Decimal and Fraction and vice versa, applied problem.

14 Concept on Ratio and Proportion-Direct and Inverse Proportion, simple applied problems.

15 Algebraic Symbols and Fundamentals - Addition, Subtraction, Multiplication and Division-Problems.

Syllabus for Sheet Metal Worker


(xiii)

Title of the Contents Common for all MR&AC SMWEngineering Trades

1 Unit

2 Fraction

3 Square root

4 Ratio & Proportion ⎯

5 Percentage

6 Algebra ⎯ ⎯

7 Material Science

8 Mass, Weight & Density ⎯

9 Speed & Velocity ⎯ ⎯

10 Work, Power & Energy ⎯ ⎯

11 Heat & Temperature ⎯

12 Basic Electricity ⎯ ⎯

Summary of Contents


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6

A[ÅhÓ AXÏLs Utßm Uôt\eLs T«t£ 1.1.03

AXÏLÞm ÑÚdLeLÞm

A[ÜLs AXÏLs AX¡uÑÚdLm

LúXôôõ©d úYpë ¡úXô _øp/¡úXô ¡Wôm kJ/kg

Ï±l©hP G¬lùTôÚs ¡úXô ¡Wôm/U¦dÏ/¨ëhPu kg/hr/N

¿[m ª.ÁhPoLs, ÁhPoLs mm, m, km¡úXô ÁhPoLs

¨û\ ¡úXô¡Wôm, ¡Wôm kg, g

úSWm ®]ô¥Ls, ¨ªPeLs, U¦Ls s, min, h

úYLm ùNu¥ÁhPôó/®]ô¥Ls cm/s, m/sÁhPo/®]ô¥Ls¡úXôÁhPôó/U¦dÏ ,ûUp/U¦dÏ km/h, mph

ØÓdLm ÁhPôó/NÕW ®]ô¥ m/s2

®ûN ¨ëhPuLs, ¡úXô¨ëhPuLs N,kN

ØùUih ¨ëhPuþÁhPôóv Nm

úYûX _÷pv J

§\u Ï§ûWj§\u,Yôhv,¡úXôYôhv Hp, W, kW

AÝjRm ¨ëhPuv/NÕW ÁhPôó N/m2

¡úXô ̈ ëhPuv/NÕW ÁhPôó kN/m2

úLôQm úW¥Vu rad

úLôQ úYLm úW¥Vu/®]ô¥ rad/s

úW¥Vu/NÕW ®]ô¥ rad/s2

JÚ ¨ªPj§p Ñtßm Ñtß RpmJÚ ®]ô¥«p Ñtßm Ñtß rev/s

ùP£Up TYo U§l× ©¬©dv Ï±ÂÓ ®[dLm

ùP£U≠u UPeÏLs Utßm AX¡u TôLeLs (Decimal multiples and parts of unit)

1012 1000000000000 ùPWô T ©p≠Vu UPeÏ

109 1000000000 _õLô G B«Wm ªp≠Vu UPeÏ

106 1000000 ùULô M ªp≠Vu UPeÏ

103 1000 ¡úXô K B«Wm UPeÏ

102 100 ùadúPô h èß UPeÏ

101 10,101 ùPLô da TjÕ UPeÏ

10-1 0.1, 10-1 ùP£ d Tj§p JÚ TeÏ

10-2 0.01 ùNu¥ c è±p JÚ TeÏ

10-3 0.001 ªp≠ m B«Wj§p JÚ TeÏ

10-6 0.000001 ûUdúWô μ ªp≠V²p JÚ TeÏ

10-9 0.000000001 SôúSô n B«Wm ªp≠V²p JÚ TeÏ

10-12 0.000000000001 ©úLô p ©p≠V²p JÚ TeÏ


7

A[ÜLs SI AXÏ →→→→→©ôõh¥x AXÏ ©ôõh¥x AXÏ →→→→→ SI AXÏ

¿[m 1 Á = 3.281 A¥ 1 A¥ = 0.3048 Á

1 ¡.Á = 0.621 ûUp 1 ûUp = 1.609 ¡.Á

úYLm 1 Á/ùNLuh = 3.281 A¥/ùNLuh 1 A¥/ùNLuh = 0.305 Á/ùNLuh

1 km/h = 0.621 mph 1 mph = 1.61 km/h

ØÓdLm 1 Á/ùNLuh2 = 3.281 A¥/ùNLuh2 1 A¥/ùNLuh2 = 0.305 Á/ùNLuh2

¨û\ 1 ¡úXô = 2.205 TÜih 1 TÜih A¥ = 0.454 ¡úXô

®ûN 1 ¨ëhPu = 0.225 TÜih A¥ 1 TÜih A¥ = 4.448 ¨ëhPu

(1 MN = 1 ùULô ¨ëhPu = 1 ªp≠Vu ̈ ëhPu)

Pôôód 1 ¨ëhPu Á= 0.738 TÜih 1 TÜih A¥/A¥= 1.355 ̈ ëhPuA¥/A¥ ÁhPôó

AÝjRm 1 ̈ ëhPu/ÁhPôó2 = 0.000145 1 TÜih A¥/AeÏXm2

TÜih A¥/AeÏXm2 = 6.896 ¡úXô ¨ëhPu/ÁhPôó2

1 Pa = 1 ¨ëhPu/ÁhPôó2

1 Tôôó = 14.5038 TÜih 1 TÜih A¥/AeÏXm2 = 6.895 ¡úXôA¥/AeÏXm2 ̈ ëhPu/ÁhPôó2

Bt\p, úYûX 1 J = 0.738 A¥ TÜih A¥ 1 A¥ TÜih A¥ = 1.3558 J1 J = 0.239 LúXôôõ 1 LúXôôõ = 4.186 J1 kJ = 0.948 Btu 1 Btu = 1.055 kJ

(1 therm = 100 000 Btu)1 kJ = 0.526 CHU 1 CHU = 1.9 kJ

§\u 1 ¡úXô Yôhv = 1.34 Ï§ûW §\u 1 Ï§ûW §\u = 0.7457 ¡úXô Yôhv

GôõùTôÚs 1km/L = 2.82 ûUp/úLXu 1 ûUp/úLXu = 0.354 km/LTVuTôÓ

Ï±l©hP 1 kg/kWh = 1.65 lb/bhp h 1 lb/bhp h = 0.606 kg/kWhGôõùTôÚs 1 litre/kWh=1.575 pt/bhp h 1 pt/bhp h = 0.631 litre/kWhTVuTôÓ

LúXôôõ©d 1 kJ/kg = 0.43 Btu/lb 1 Btu/lb = 2.326 kJ/kgúYpë 1 kJ/kg = 0.239 CHU/lb 1 CHU/lb = 4.188 kJ/kg

NoYúRN Øû\ AXÏLs Utßm ©ôõh¥x AXÏLs (SI units and the British units)

T¦Uû] LQdÏ Utßm A±®Vp : (NSQF) T«t£ 1.1.03


8

Nm2

Nm2

M

ùYlT Bt\pùYlT A[Ü

AÝjRm P ¨ëhPu/ÁhPôó2

¨ëhPu/ÁhPôóó2

YûWVû\ÙPu AXÏLû[ A[dL TZÏRp (Units in measuring practice with definitions)

A[ÜLs AXÏ ®[dLm

N 1 ¡úXô ¨û\Ùs[ JÚ ùTôÚ°uÁÕ ùNVpThÓ 1m/s2 ØÓdLjûRHtTÓjÕm ®ûN 1 ¨ëhPuBÏm.JÚ ùTôÚ°u ¨û\1 ¡úXô1 ̈ ëhPu = 1 ¡úXô ÁhPôó/ùNLih2

1 ̈ ëhPu/ÁhPôó2 (1 pascal)AÝjRj§tÏ NUUô]Õ. ARôYÕ1 ̈ ëhPu ®ûN JÚ NÕW ÁhPôóTWl©tÏ ùNeÏjRôLl ùNVpTÓ¡\Õ.

TôvLp Pa 1 Pa = 1 ¨ëhPu/ÁhPo2 1 Tôo (1bar)GuTÕ 100 000 Pa dLô] £\l× ùTVoBÏm.

1 ̈ ëhPu/ÁhPôó2 (1 TôvLp)ùUdLô²dLp v¥Wv RûLÜ,1 ̈ ëhPu RûLYôL JÚ NÕWÁhPoTWl©u ÁÕ ùNVpTÓjRlTÓ¡\Õ.ùTô±«V≠p TX ©¬ÜL°p CkRCVk§W RûLÜ Utßm Eß§¨ëhPu/ ÁhP¬p Ï±dLlTÓ¡\Õ.1 ̈ ëhPu/ÁhPôó2 = 1000 000 TôvLp= 1 MPa®ûN«u §ûN«p 1 N ®ûNûVTVuTÓj§ AkR §ûN«p 1 ÁSLojÕm úYûX«u A[Ü 1 _÷p -dÏ NUm.1 _÷p = 1 ¨ëhPu Á = 1 Ws = 1 kgm2/s2

3600 000 _÷p = 1 ¡úXô Yôhv AYôó

Nm 1 ̈ ëhPu úUôùUuh BlúTôôóÑdÏ NUUô]Õ.

J CÕ JÚ ¨ëhPu Utßm 1 ÁhPôóùSm×úLôp×Vj§u ùTÚdÏjùRôûLVôÏm. 1 ¨ëhPu ÁhPôó = 1_øp = 1 Ws = 1 ¡úXô¡Wôm ÁhPôó2/®]ô¥2

W 1 ®]ô¥ úSWj§p 1 _øp Bt\pUôtßYRtÏj úRûYVô] NU A[Ü§\ú] 1 Yôh G]lTÓ¡\Õ.ªu§\àdLô] ®YWdÏ±l×LsúYôph Bm©Vo Guß YôhAX¡tÏ T§XôL AûZdLlTÓ¡\Õ.

ùYlT KhPm ø 1 W = 1 J/s = 1 Nm s = 1 VA

NôRôWQ RûLÜCÝj RûLÜ (A)CßdLj RûLÜ,ùYhÓjRûLÜ

®ûN F ¨ëhPu

W _÷p J

¨ëhPuÁhPo_øp

úUôùUihBl úTôôóv

(Pôod)

P Yôh§\uBt\pJhPm



9

_øp 1 ¡úXô ¨û\ûV ØÝûUVôL/¡úXô¡Wôm GôõjÕ ùY°lTÓjÕm 1 _øp Bt\p

1 _øp/¡úXô¡WôØdÏ NUUô]ùYlTUôÏm.

1 kwh úYûXdÏj úRûYVô]/ ¡WômGôõùTôÚs 1 ¡Wôm /¡úXôYôhU¦dÏf NUUôÏm

ùYlT ¨ûX T ùLp®u K êuß ×s° Ri½ôõuùRôóúUôûP]ªd ùYlTSõûX«u 273 þ 16 Cp JÚ TeÏRôu ùLp®uG]lTÓm.

ªuú]ôhPm I Bm©Vôó A JÚ Bm©Vôó ªuNôWm GuTÕCWiÓ CûQVô] LPj§LÞdÏCûPúV Es[ çWm JÚ ÁhPôõpGXdhúWôûP]ªd ®ûNûV 0.2.10¨ëhPu /JÚ ÁhPôó ¿[j§tÏùLôiÓ YÚYRôÏm.

V úYôph V ùUhPô≠d LiPdPôõu CWiÓ×s°LÞdÏ CûPúV,1 W Nd§ êXmLWih¥u TXm 1 A BÏm. C§p 1Kph GuTÕ GXd¥ôõdúYôpúP_õdÏ NUm BÏm.

R Ohm Ω ùUhPô≠d LiPdPôõu CWiÓ×s°LÞdÏ CûPúV 1Aªuú]ôhPm, 1 V ªu]ÝjRj§pùNpÛm ùTôÝÕ HtTÓm 1 KmªuNôW ªuRûPdÏf NUm.

G ºùUuv S JÚ ºùUuv GuTÕ JÚ KmLiPdPôõu GXd¥ôõd ùW£vPuvÑdÏ NUUô]Õ.

Q áÛml C 1 áÛml GuTÕ GXdhôõ£h¥«uBm©Vôó ®]ô¥ AS A[Ü, ARu KhPm, LPj§«u

ÏßdÏ ùYhÓlTWl©p1s þp ,1AªuNôW ªuú]ôhPUôÏm.

H/μ

gkwh P

Jkg

ùYlT GiûQU§l©ÓRp

GôõùTôÚsTVuTôÓ

ªuNôW ªu]ÝjRm

ªuNôW ªuRûP

ªuNôW LiPdPuv

ªuNôWj§u A[Ü


¡Wôm/ ¡úXôYôh

U¦


10

RNU ùTÚdLp Utßm UßT¥ÙmùTÚdÏYRtÏ Øu× Es[ûY (Prefixes fordecimal multiples and submultiples)

1 ùULôTôvLp = 1 MPa = 1000000 TôvLp

1 ¡úXôYôh = 1 kW = 1000 Yôhv

1 ùadúPô≠hPôó= 1 hL = 100 ≠hPo

ùPdLô ̈ ëhPu = 1 daN = 10 ̈ ëhPu

ùP£ ÁhPôó = 1 dm = 0.1 ÁhPo

1 ùNu¥ÁhPôó = 1 cm = 0.01 ÁhPo

1 ªp≠ÁhPôó = 1 mm = 0.001 ÁhPo

1 ûUdúWôÁhPôó = 1 um = 0.000001 ÁhPo

ETúVôLm

UôtßYRtLô] LôW¦Ls (Conversion factors)

1 AeÏXm = 25.4 ª.Á

1 ª.Á = 0.03937 AeÏXm

1 ÁhPôó = 39.37 AeÏXm

1 ûUdWôu = 0.00003937AeÏXm

1 ¡úXôÁhPôó = 0.621 ûUpLs

1 TÜih = 453.6 ¡Wôm

1 ¡úXô = 2.205 TÜiÓLs

1 ùUhôõdPu = 0.98 Pu

TWl©uAXÏ (Units of area)

CVt©Vp A[ÜL°u AXÏ (Units ofphysical quantities)

¿[j§u AXÏ (Units of length)

NÕW ªp≠ ÁhPo 1 mm2

NÕW ùNu¥ ÁhPo 1 cm2 = 100 ª.Á2

NÕW ùP£ ÁhPo 1 dm2 = 100 ùN.Á2

NÕW ÁhPo 1 m2 = 100 ùP.Á2

Ho (Are) 1 a = 100 Á2

ùadúPo 1 ha = 100 Ho(a)

NÕW ¡úXôÁhPo 1 km2 = 100 ùadúPo

NÕW AeÏXm 1 sq.in = 6.45 ùN.Á2

NÕW A¥ 1 sq.ft = 0.093 Á2

NÕW L_m 1 sq.yd = 0.84 Á2

NÕW ÁhPo 1 m2 = 10.76 A¥2

HdLo 1 = 40.5 Ho

1 HdLo = 100 ùNuh

1 ùNuh = 436 N.A¥

1 ¡WÜih = 2400 N.A¥

ûUdWôu 1 μ = 0.001 ª.Á

ªp≠ ÁhPôó 1 mm = 1000 μ

ùNu¥ ÁhPôó 1 cm = 10 ª.Á

ùP£ ÁhPôó 1 dm = 10 ùN.Á

ÁhPôó 1 m = 10 ùP.Á

¡úXô ÁhPôó 1 km = 1000 Á

AeÏXm 1" = 25.4 ª.Á

A¥ 1" = 0.305 Á

ùL_m 1 Yd = 0.914 Á

Sôh¥Lp ûUp 1 NM = 1852 Á

_õúVô¡Wôl©dLp 1 = 1855.4 ÁûUp

1 ùadPo = 2.47 HdLo

1 HdLo = 0.4047 ùadPo

1 ùadPo = 10000 N.ÁhPo

GûP«u AXÏ (Units of weight)


úSWm (Time)ùNLih (®]ô¥) 1 S

¨ªPm 1 ¨ªPm = 60 ®]ô¥

U¦ 1 U¦ = 60 ¨ªPm

ªp≠ ¡Wômþ®ûN 1 mgf¡Wômþ®ûN 1 gf 1000 mgf¡úXô ¡Wômþ®ûN 1 kgf = 1000 gfPu 1 t = 1000 kgfAÜuv 1 = 28.35 gfTÜih 1 lbs = 0.454 kgf¿iP Pu 1 = 1016 kgfÏß¡V Pu 1 = 907 kgf


11

L] A[Ü Utßm ØLjRp A[ÜL°uAXÏLs (Units of volume and capacity)

L] ªp≠ ÁhPôó mm3

L] ùNu¥ ÁhPôó 1 cm3 = 1000 ª.Á3

L] ùP£ ÁhPôó 1 dm3 = 1000 ùP.Á3

L] ÁhPôó 1 m3 = 1000 ùP.Á3

≠hPôó 1 l = 1 ùP.Á3

ùadúPô ≠hPôó 1 hl = 100 ≠hPo

L] AeÏXm 1 cu. in = 16.387 ùN.Á3

L] A¥ 1 cu. ft = 28317 ùN.Á3

úLXu (©ôõh¥x) 1 gal = 4.54 ≠hPo

1L] ÁhPôó 1 m3 = 1000 ≠hPo

1000 L] ùN.Á 1000 cm3 = 1 ≠hPo

1 L] A¥ 1 ft3 = 6.25 úLXu

1 ≠hPôó 1It = 0.22 úLXu

úLôQm (Angle)

1 ùNu¥v£Up AXÏ

1 ùNeúLôQm = 100 ¡úWÓ (100g)

1 ¥¡ôõ (1g) = 100 ̈ ªPm (100’)

1 ¨ªPm (1’) = 100 ùNLuh (100”)

2 ùNdNô_õUp AXÏ

1 ùNeúLôQm = 90 ¥¡¬ (900)

1 ¥¡¬ (10) = 60 ̈ ªPm (60’)

1 ¨ªPm (1’) = 60 ®]ô¥ (60”)

1800

π

π 180

3 YhP AXÏ

úW¥Vu

úW¥VàdÏm Utßm ¥¡¬dÏm CûPúVEs[ E\ÜLs

1 úW¥Vu =

1800 = π úW¥Vu;

1 ¥¡¬ = úW¥Vu

úYûX (Work)

¡úXô¡Wôm-®ûN 1 kgfm = 9.80665 J

ÁhPo 1 kgfm = 9.80665 Ws

_øp 1 J = 1 Nm

Yôh- ùNLih 1 Ws = 0.102 kgfm

¡úXôYôh aYo 1 kWh = 3.6 x 106 J= 859.8845 kcalIT

I.T.¡úXô LúXô¬ 1 kcalIT = 426.kgfm

§\u (Power)

¡úXô¡Wôm ®ûN ÁhPôó/®]ô¥

1 kgfm/s = 9.80665 W¡úXô Yôh 1 ¡úXô Yôh =

1000 Yôh = 1000 J/s

= 102 kgfm/s (úRôWôVUôL)

ùUh¬d Ï§ûW 1 Ï§ûW §\u = 75 kgfm/s

§\u = 0.736 kW

1 LúXô¬ = 4.187J

I.T.¡úXô LúXô¬ / aYo

= 1 ¡úXô LúXô¬IT/h

= 1.163 Yôhv

101325 760

TôvLp 1 TôvLp = 1 ̈ ëhPu/ÁhPo2 1 atm = 101325 TôvLp

Tôo 1 Tôo = 10 ¨ëhPu/ùNÁ2 = 100000 Pa–Torr 1 torr =

AhUôv©Vo 1 atm = 1 kgf/cm2 1 kgf/cm2 = 735.6 ª.Á ùUoÏ¬

AÝjRm (Pressure)

= 133.32 pa



12

l ¿[m m ÁhPo mh EVWm m ÁhPo mb ALXm m ÁhPo mr BWm m ÁhPo md ®hPm m ÁhPo md,δ ÑY¬u R¥Uu m ÁhPo mS Y¯«u ¿[m m ÁhPo mA (S) TWlT[Ü m2 NÕW ÁhPo m2

V (v) L] A[Ü m3 L] ÁhPo m3

α,β,γ etc úLôQm ° úW¥Vu (1 rad = 57.30) radλ AûX ¿[m km ¡úXôÁhPo kml,la ùNLih úUôùUuh cm4 Metre to the fourthpower m4

Bl H¬Vô

NoYúRNAXÏLsNoYúRNAXÏ

Ï±ÂÓLs

CVt©VpA[ÜLs

YZdLUô]Ï±ÂÓLs

Ï±ÂÓ

_õúVôª§ A[ÜLs (Geometrical quantities)

m ¨û\ kg kg ¡úXô ¡Wôm kgc,ρ APoj§ g/cm3 ¡úXô ¡Wôm/L] ÁhPo ókg/m3

l,J úUôùUuh Bl C]o£Vô kg, m2 ¨ëhPu ÁhPôó Nm

¨û\ (Mass)

T úSWm (A) úSW CûPùY° s ®]ô¥ snu ùWôhúPN]p AûXY¬ûN l/min ùW£lúWôdLp ®]ô¥ l/su,v,w,c §ûN úYLm m/min ÁhPo/®]ô¥ m/sω úLôQ §ûN úYLm rad/s úW¥Vu/®]ô¥ rad/sg Free fall ØÓdLm m/s2 ÁhPo/®]ô¥2 m/s2

a ØÓdLm m/s2 ÁhPo/®]ô¥2 m/s2

Ïû\ ØÓdLm m/s2 ÁhPo/®]ô¥2 m/s2

F ®ûN kgf ¨ëhPu (1kgf = 9.80665N) N

G(P,W) GûP kgf ¨ëhPu N

γ Ï±l©hP GûP kgf/m3 ¨ëhPu/L] ÁhPo N/m3

M CVdL ®ûN

(®ûN x çWm) kgf.m ¨ëhPu ÁhPo N.m

P AÝjRm (®ûN/TWlT[Ü) kgf/cm2 TôvLp, ¨ëhPu/N.Á Pa,N/m2

p NôRôWQ RûLÜ kgf/mm2 Tôo (1Tôo=10N/m)

τ p ùYhÓ RûLÜ kgf/mm2 Tôo

E Áh£«Vp ÏQLm kgf/mm2 ¨ëhPu/N.Á N/m2

G ùYhÓ ÏQLm kgf/mm2 ¨ëhPu/N.Á N/m2

μ (f) EWôn®u ùTÚdL ÏQm No Unit

úSWm (Time)

®ûN Utßm AÝjRm (Force and Pressure)



13

ùNu¥ ¡úWÓ (0C) 00C 1000CúTWuÍh (0F) 320F 2120F

ùLp®u (K) 273K 373KÃUo (0R) 00R 800R

ùYlT ¨ûX (Temperature)

vúLp Eû\ ¨ûX ùLô§ ¨ûX

°R 80

°C100= = = K- 273

100 °F- 32 180

A,W úYûX kgfm _øp (1 _øp=1 ¨ëhPu.Á) J (Nm)

P §\u kgfm/s Yôh W (J/s)

E,W Bt\p kgfm _øp J (Nm)

η TV]ß §\u - - -

W,A,E,Q ùYlT A[Ü kcal _øp J

ùYlTm, úYûX, Bt\p, ®ûN (Heat, Work, Energy, Force)

ùYlT Gi kcal/kgf°C _øp/¨ëhPu/ J/N.°K

¥¡¬ ùLp®u

ùYlTdLPjRp kcal/mh°C _øp ÁhPo/ J/ms°K

®ûN (Force) ®]ô¥/¥¡¬ ùLp®u

C.G.S. Øû\«p : ®ûN (ûPu) = ̈ û\ (gm) X ØÓdLm (ùN.Á/®]ô¥2)

F.P.S. Øû\«p: ®ûN (TÜiPp) = ̈ û\ (Ib) X ØÓdLm (A¥/®]ô¥2)

M.K.S Øû\«p : ®ûN (¨ëhPu) = ¨û\ (Kg) x ØÓdLm (Á/®]ô¥2)

ARu ùTôÚs 1 ûPu = 1 ¡Wôm x1 ùN.Á/®]ô¥2

1 TÜiPp = 1 TÜuh x 1 A¥/®]ô¥2

1 ̈ ëhPu = 1 ¡úXô x 1 ÁhPo/®]ô¥2 = 105

ûPuLs

1 ¡Wôm GûP = 981 ûPuLs

1 TÜih GûP = 32 TÜiPp

1 ¡úXô GûP = 9.81 ¨ëhPuLs

C

V ªu ùTôhùPu£Vp V úYôph V(W/A)

E ªu²VdÏ ®ûN V úYôph V(W/A)

I ªuú]ôhPm A Bm©Vo A

R ªu RûP Ω Km Ω (V/A)

e CûQ ªu RûP Ω m Km ÁhPo Vm/A

G LuPdPuv Ω-1 ºùUuv S

ªu A[ÜLs (Electrical Quantities)



14

¿[m, ¨û\, ®ûN, úYûX, §\u Utßm Bt\ûX UôtßRpT«t£ 1.1.04

1 ¸úZ ùLôÓdLlThÓs[ûYLû[ UôtßL

a 5 ùL_eLû[ ÁhPWôL Uôtß

b 15 ûUpLû[ ¡úXô ÁhPWôL Uôtß

c 7 ÁhPûW ùL_UôL Uôtß

d 320 ¡úXô ÁhPûW ûUXôL Uôtß

2 UôtßL

a 5 TÜiÓLû[ ¡úXô¡WôUôL Uôtß

b 8.5 ¡úXô¡WôûU TÜiPôL Uôtß

c 5 AÜuûN ¡WôUôL Uôtß

d 16 PuLû[ ¡úXô¡WôUôL Uôtß

3 UôtßL

a 40 AeÏXjûR ùNi¥ÁhPWôL Uôtß

b 12 A¥ûV ÁhPWôL Uôtß

c 5 ÁhPoLû[ AeÏXUôL Uôtß

d 8 ÁhPoLû[ A¥VôL Uôtß

4 UôtßL

a 234 L]ÁhPûW úLX]ôL Uôtß

b 2 L]A¥ûV ≠hPWôL Uôtß

c 2.5 úLXuLû[ ≠hPWôL Uôtß

d 5 ≠hPoLû[ úLX]ôL Uôtß

5 ¸rLiP úLs®LÞdÏ ®ûP A°dLÜm

a 120°C = ______ °F.

b 8 ª.Á = ______ AeÏXeLs

12 ª.Á =______ AeÏXeLs

6 UôtßL Utßm LiÓ©¥dLÜm

JÚ Lôo 40 ûUpLs TVQm ùNnYRtÏJÚ úLXu G¬ ùTôÚs úRûYlTÓ¡\Õ.

CúR Lôo 120 ¡úXô ÁhPo TVQmùNnYRtÏ GjRû] ≠hPo G¬ùTôÚsúRûYlTÓm.

7 ùLôÓdLlThP ùUh¬d AXÏLÞdÏN¬Vô] ©¬h¥x AXÏLs VôûY?

a ®]ô¥, ¨ªPm, U¦

b ¡Wôm, ¡úXô¡Wôm

c ≠hPov, L] ÁhPoLs

d NÕW ùNu¥ÁhPo, NÕW ¡úXô ÁhPo

8 ¸rLiP ÑÚdLj§u ®¬YôdLj§û]GÝRÜm

a km/L

b N/m2

c KW

d m/S2

e RPM9 ¸r LiPYtû\ NoYúRN AXÏL°p Uôt±

GÝRÜm

a ¿[m

i 3.4 ÁhPo = ______ ª.Á

ii 1.2 ÁhPo = ______ ùN.Á

iii 0.8 ÁhPo = ______ ª.Á

iv 0.02 ¡úXô ÁhPo = ______ ùN.Á

v 10.2 ¡úXô ÁhPo = ______ ûUp

vi 6 ÁhPo = ______ ¡.ÁhPo

vii 18 ÁhPo = ______ ª.Á

viii 450 ÁhPo = ______ ¡. ÁhPo

ix 85 ùN.Á = ______ ¡. ÁhPo

x 0.06 ¡úXô ÁhPo = ______ ª.Á

b ¨û\

i 650 ¡Wôm = ______ ¡úXô ¡Wôm

ii 300 ùNu¥¡Wôm = ______ ¡Wôm

iii 8 ¡Wôm = ______ ùP£ ¡Wôm

iv 120 ªp≠¡Wôm = ______ ¡Wôm

v 8 ùPdLô¡Wôm = ______ ªp≠ ¡Wôm

vi 2.5 ¡Wôm = ______ ªp≠ ¡Wôm

vii 2.5 ¡Wôm = ______ ¡úXô ¡Wôm

viii 20 ùNu¥ ¡Wôm = ______ ªp≠ ¡Wôm

ix 0.05 ùUhôõd Pu = ______ ¡úXô ¡Wôm

c ®ûN

i 1.2 ̈ ëhPu = ______¡úXô ¡Wôm

ii 2.6 ̈ ëhPu = ______ ¡úXô ¡Wôm

iii 800 ̈ ëhPu = ____ ¡úXô ¨ëhPu

iv 14.5 ¡úXô ¡Wôm = ______ ̈ ëhPu

v 25 ¡úXô ¡Wôm = ______ ̈ ëhPu


15

d úYûX, Bt\p, ùYlT A[Ü

i 2 ̈ ëhPu ÁhPôó = ______ ̈ ëhPuùNu¥ ÁhPôó

ii 50 ̈ ëhPu ùNu¥ ÁhPôó=_________¨ëhPu ÁhPôó

iii 120 ¡úXô _øp = ______ _øp

iv 40 _øp = ______ ¡úXô _øp

v 300 YôhvAYôó = ______ ¡úXô Yôhv AYo

e §\u

i 200 ùULô Yôhv = ______ Yôhv

ii 0.2 ¡úXô Yôhv = ______ Yôhv

iii 300 ¡úXô Yôhv =____ùULô Yôhv

iv 2.106 Yôhv =____ùULô Yôhv

v 6.10-4 ¡úXô Yôhv = ______ Yôhv

vi 2 Yôhv =____¡úXô Yôhv

vii 350 Yôhv =____¡úXô Yôhv

viii 0.08 Yôhv =____¡úXô Yôhv

ix 2 x 10-3 ¡úXô Yôhv=______ Yôhv

x 0.04 Yôhv =____ùULô Yôhv

f úRûYdÏ Ht\Yôß UôtßL

i 3 ̈ ëhPu ÁhPôó = ______ _øp

ii 2 _øp = ______ Ws

iii 12 _øp = ______¡úXô _øp

iv 3 ̈ ëhPu = _____øp/®]ô¥

v 5 ̈ ëhPu =___________¡úXô ̈ ëhPu

vi 3 ¡úXô _øp = ______ ̈ ëhPu ÁhPo

vii 18 _øp/®]ô¥ = ______ Yôhv

viii 12 Yôhv = __________ _øp/ ®]ô¥

ix ¡úXô _øp/®]ô¥ = ______ ¨ëhPu ÁhPôó/®]ô¥



16

LôW¦Ls, HCF, LCM Utßm LQdÏLs T«t£ 1.2.05

TLô Gi Utßm ØÝ GiLs (Primenumbers and whole numbers)

LôW¦ (Factor)

LôW¦ GuTÕ JÚ £±V Gi. CRu êXmùTôõV GiLû[ NôõVôL YÏdL CVÛm.ERôWQm

24, 72, 100 GiL°u LôW¦Lû[d LiÓ©¥

24 = 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

100 = 2 x 2 x 5 x 5

2,3,5 B¡V GiLs LôW¦LsBÏm.

TLô LôW¦«u YûWVû\ (Definintion of aprime factor)

TLô LôW¦ GuTÕ JÚ Gi. AûR TLôGiQôp YÏjRôp LôW¦ ¡ûPdÏm.ERôWQm

57 = 3 x 19

3 Utßm 19 B¡V GiLs TLô LôW¦L[ôÏm.

3 Utßm 19 B¡V GiLû[ TLô GiTh¥V≠p YÚYRôp AYtû\ TLô GußmAûZdLXôm.

H.C.F GuTRu YûWVû\ (Definition of H.C.F)

CÕ A§LThN ùTôÕd LôW¦. GiL°uùRôÏl©p Es[ GpXô GiLÞm NôõVôLYÏdLlTÓm LôW¦VôÏm. ERôWQm.

24, 72, 100 B¡V GiL°u HCFI LiÓ©¥

24 = 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

100 = 2 x 2 x 5 x 5

êuß GiL°Ûm ùTôÕYô] LôW¦LsBÏm. ARôYÕ 2 x 2 = 4. So HCF = 4.

Áf£ß UPeÏ GuTRu YûWVûW(Definition of L.C.M)

ªLf£±V ùTôÕYô] ùTÚdÏ Gi

Áf£ß UPe¡àûPV ùRôÏl× Gi £±VGiQôL CÚdÏm. ùLôÓdLlThPùRôÏl©u JqùYôÚ GiÔm ÁRmCpXôUp CÚdÏm. ERôWQm

• ¸r LiP GiLÞdÏ LôW¦Lû[LiÓ©¥

7,17,20,66,128

7,17 - B¡V CWiÓm TLô GiûQf úNôókRÕ.CûYLÞdÏ LôW¦Ls úRûY CpûX.B]ôp CûY JúW C]m.

20 þu LôW¦Ls = 2 x 2 x 5

2 663 33

11

2 1282 642 322 162 82 4

2

66 þu LôW¦Ls = 2 x 3 x 11

2 783 39

13

128 þu LôW¦Ls = 2 x 2 x 2 x 2 x 2 x 2 x 2

2 1282 642 322 162 82 4 2

• 3 ØRp 29 YûW Es[ GiL°u TLôGiLû[ úRôóÜ ùNn.

3,5,7,11,13,17,19,23,29,

• ¸rdLiP ÏÝ GiL°u (78, 128, 196) HCF-Id LiÓ©¥

78=2x3x13

2 1962 98

49

2 202 10

5

128=2x2x2x2x2x2x2

196 = 2x2x49

LCM = Áf£ß UPeÏ Á.£.U

HCF = A§LThN ùTôÕdLôW¦A.ùTô.Lô


17

2 84, 92, 762 42, 46, 383 21, 23, 19

7, 23, 19

2 36, 108, 602 18, 54, 303 9, 27, 153 3, 9, 5 1, 3, 5


HCF = 2

• 84,92,76 B¡V GiL°u Áf£ß UPeûLLiÓ©¥ (LCM)

LCM =

Áf£ß UPeÏ = 2 x 2 x 3 x 7 x 23 x 19 = 36708

• 36, 108, 60 B¡V GiL°u Áf£ß UPeûLLiÓ©¥ (LCM)

Áf£ß UPe¡u Gi (LCM)

36, 108, 60 = 2 x 2 x 3 x 3 x 3 x 5 = 540

©u]eLû[d L¯dÏm ùTôÝÕ UtßmáhÓm ùTôÝÕ LCM Utßm HCFLiÓ©¥lTRu úRûY HtTÓm.


18

©u]eLs T«t£ 1.2.06

®YWm (Description)

Ïû\kR A[Ü B]ôp AûY ØÝ Gi ApX.

ERôWQm Gu\ ©u]m GuTÕ ùRôÏ§

Utßm TÏ§ûV ùLôiÓs[Õ.

ùRôÏ§/TÏ§ (Numerator/Denominator)

úLôh¥tÏ úUúX Es[ Gi NôRôWQ©u]j§p ¸úZ Es[ Gi¦u U§l©pEs[ TeLôÏm ERôWQm.

C§p 1,3,7 - GuTûY ùRôÏ§VôÏm (Numerators)4,12 - GuTûY TÏ§VôÏm (Denominators).

©u]m : LÚjÕÚ (Fraction: Concept)

JqùYôÚ GiûQÙm ©u]UôL©W§¨§jÕYlTÓjRXôm. ERôWQm.

, JÚ ØÝ GiûQ ©u]UôL

©W§¨§jÕYlTÓjRXôm. (TPm 1)

ùTÚdLp (Multiplication)

©u]eLû[ ùTÚdÏm ùTôÝÕ GpXôTÏ§Lû[Ùm ùTÚd¡]ôp, TÏ§L°uùTÚdÏ ùRôûL ¡ûPdÏm Utßm GpXôùRôÏ§Lû[Ùm ùTÚd¡]ôp, ùRôÏ§L°uùTÚdÏ ùRôûL ¡ûPdÏm (TPm 3)

©u]m: U§l× (Fraction:Value)

©u]j§u TÏ§ûVÙm, ùRôÏ§ûVÙm JúWGiQôp YÏjRôúXô ApXÕùTÚd¡]ôúXô ©u]j§u U§l× Uô\ôÕ(TPm 2)

YÏjRp (Division)

JÚ ©u]jûR Utù\ôÚ ©u]jRôp YÏdL.YÏdÏm ©u]jûR RûX ¸ZôL Uôt±YÏTÓm ©u]júRôÓ ùTÚdL úYiÓm.(TPm 4)

áhPp Utßm L¯jRp (Addition andSubraction)

©u]eLû[ áhP (A) L¯dL AYt±u TÏ§NUUôL CÚdL úYiÓm. TÏ§Ls ANUUôLCÚl©u AûR Áf£ß UPeLô] TÏ§VôLUôt\ úYiÓm. CûR JqùYôÚ ©u]j§uTÏ§VôÛm YÏjÕ DûY ùRôÏ§Vôp ùTÚd¡áhP úYiÓm (TPm 5)


19

ERôWQm

• ùTÚdLp

• YÏjRp

• áhPp

p CÚkÕ I L¯dLÜm

©u]eL°u YûLLs (Types of fractions)

• RÏ©u]j§u ùRôÏ§ TÏ§ûV®PGlùTôØÕm Ïû\YôLLúY CÚdÏm.

RLô©u]j§u ùRôÏ§ TÏ§ûV®PA§LUôL CÚdÏm.

LXl× ©u]m GuTÕ JÚ ØÝ GiÔm,RÏ©u]Øm LXkR Jo GiQôÏm.

©u]jûR áhÓRp (Addition of fraction)

áhPp

CkR ©u]jûR áhP, Sôm 2,8,12 B¡VTÏ§L°u Áf£ß UPeûL (LCM) LiÓ ©¥dLúYiÓm.

2,8,12 u Áf£ß UPeûL LiÓ ©¥dLÜm.

vùPl 1 Áf£ß UPeÏ Gi

2 2,8,122 1,4,6

1,2,3

LôW¦Ls 2,2,2,3

BûLVôp Áf£ß UPeÏ Gi

= 2 x 2 x 2 x 3 = 24,

vùPl 2

©u]jûR L¯jRp (Subtraction of fractions)

≠ÚkÕ - I L¯ (A)

vùPl 1: ØÝ GiûQ ØR≠p L¯dLÜm 17 - 9 = 8

vùPl 2 : 16,32 = 32 dLô] Áf£ß UPeÏ (LCM) 32

32 Gu\ Gi 16 Gu\ GiQôp YÏTÓYRôp

Gu\ ©u]m ¡ûPdÏm.

vùPl 1 u T¥ ØÝ GiûQ úNodÏmùTôÝÕ.

SUdÏd¡ûPlTÕ

NôRôWQ ©u]eLs (Common fractions)

áhPp Ï± Utßm L¯jRp Ï± ùLôiPLQdÏLs.

ERôWQm

¾oÜ Lôi

¸r LiP ®§Lû[ LûP©¥dLÜm.

1 GpXô ØÝ GiLû[Ùm áhPÜm

2 áhPp Ï± (+) Es[ GpXô GiLû[ÙmáhPÜm.

3 L¯jRp Ï± (-- - -) Es[ GpXô GiLû[ÙmáhPÜm.

4 GpXô TÏ§L°u Á.£.U -ûYLiÓ©¥dLÜm.

¾oÜ

vùPl 1 : ØÝ GiLû[ áhPÜm= 3 + 6 - 4 = 5

vùPl 2 : ©u]eLû[ áhPÜm= 3/4 + 7/8 - 5/16 - 9/32

Á.£.U. Gi: 4,8,16,32 is 32

3217

16 7



20

vùPl 3: ÁiÓm ØÝ GiLú[ôÓ áhÓmùTôÝÕ..

SUdÏ ¡ûPlTÕ

AûPl×Ls Utßm ARu ¾oÜLs (Bracketsand their solution)

CWiÓ ApXÕ CWi¥tÏ úUtThP ©u]dáßLû[ £XNUVm áhÓYRtúLô ApXÕL¯lTRtúLô AûPl×dÏ± TVuTÓjRlTÓ¡\Õ. AûPl©tÏs CÚlTûYLû[ ¾oÜLôiTRtÏ ‘BODMAS’ Gu\ ®§TVuTÓjRlTÓ¡\Õ.

BODMAS ®§

• B - ©WôdLh CûR ØR≠p ùNnV úYiÓm.

• O -of CWiPôYRôL

• D - YÏjRp êu\ôYÕ

• M - ùTÚdLp SôuLôYÕ

• A - áhPp IkRôYRôL

• S - L¯jRp LûP£VôL ùNnV úYiÓm

AûPl×Ls Es[ LQdÏ

¾oÜ Lôi

• YÏjRp (Division)

a

b

• áhPp (Additions)

• L¯jRp (Subract)

¸rLiP vùPl©û] LûP©¥dLÜm.

( ) 1 Es TdL AûPlûT ¾odLÜm ( )

2 ùTÚdLp Utßm YÏjRûX Ju\ôL¾odLÜm

3 áhPp Utßm L¯jRûX Ju\ôL¾odLÜm

{ } 4 LûP£ ¨ûXdÏ úTôÏm ØuYû[Yô] AûPlûT ¾odLÜm.

[ ] 5 LûP£VôL NÕW AûPlûT ¾odLÜm.

ERôWQeLs

NôRôWQ ©u]eLs (Common fractions)

• ùTÚdLp (Multiply)

a

b

14

3

7

4x

8

3

7

4by

8

3==

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛ −+−+

21

872116810

12308

123810

8

315810

8

31580

==

=

+

××

⎥⎦⎤

⎢⎣⎡ ×

⎥⎦

⎤⎢⎣

⎡⎭⎬⎫

⎩⎨⎧= 1

2

1367

4

2367

4

1470

4

4956

4

11256

4

119456

4

1

2

119456

=

=

=

×=

×=

+−+=

−+−+

⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡

⎥⎦

⎤⎢⎣

⎡⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛

AûPl×Ls Es[ LQdÏ (Bracket problems)

• ¾ôóÜ Lôi

‘BODMAS’ ®§ûV TVuTÓj§ ¾oÜ LôiL.

• ‘BODMAS’ ®§ûV TVuTÓj§ ¾oÜ LôiL.



21

RNU ©u]eLs T«t£ 1.2.07

®[dLm (Description)

RNU ©u]m GuTÕ JÚYûL ©u]mARàûPV TÏ§ 10 (A) 10 u ùTÚdÏ ùRôûL(ARôYÕ) 10,100,1000, 10,000 ØR≠VûY RNUGiLÞdLô] ùTôÚ[ôÏm.

12.3256 GuTÕ

©W§¨§jÕYm (Representation)

C§p TÏ§ ¡ûPVôÕ TÏ§«u A[ÜU§l©û]l ùTôÚjÕ, RNU ×s°LsTpúYß ¨ûXL°p Ï±l©PlTÓ¡\Õ.

ERôWQm.

3.648

1000

36480.0127,

10000

1270.35

100

350.5,

10

5====

áhPp Utßm L¯jRp (Addition andsubtraction)

RNU ©u]j§u ×s°Ls ùNeÏjÕY¬ûN«p ûYdLlTÓ¡\Õ. JqùYôÚ©u]jûRÙm áhÓm ùTôÝÕ (A) L¯dÏmùTôÝÕ AÓjRÓjÕ ARu ¸rûYdLlTÓ¡\Õ. CRu êXm GpXô RNU×s°LÞm úSoY¬ûN«p ûYdLlTÓ¡\Õ.áhÓm ùTôÝúRô (A) L¯dÏm úTôúRô ØÝGiLÞdÏ LûP©¥lTÕ úTôp RNU×s°L°u Y¬ûNdÏ ¸úZ Ï±jÕ ®ûPA°dL úYiÓm.

RNU ©u]eLs JußdÏ Ïû\YôL CÚkRôp,RNU ×s°dÏ Øu× é_óVm Ï±dLúYiÓm.ERôWQm: 45/100 = 0.45 (ùYßUú] .45 Gu\GÝRdáPôÕ)

áhÓL 0.375 + 3.686

0.375

3.686

4.061

L¯dLÜm 22.61 p CÚkÕ 18.72 I L¯dLÜm.

22.61

18.72 3.89

ùTÚdLp (Multiplication)

RNU ×s°Lû[ LiÓùLôs[ôUp ØÝGiLû[ ùTÚdL úYiÓm. RNU ×s°dÏ

YXÕ TdLm ùUôjRm GjRû] CXdLmEs[Õ GuTûR LY²dL úYiÓm. CkRRNU ×s°ûV YXÕ TdLj§p CÚkÕ Ï±dLúYiÓm.

ùTÚdÏL 2.5 by 1.25

= 25 x 125 = 3125. YXÕ TdLj§p RNU×s°«u áhÓj ùRôûL 3. AR]ôp ARu®ûP 3.125

YÏjRp (Division)

ØÝ GiQôL Uôt\ RNU ×s°ûV YXÕTdLUôL SLôój§ ûYdL úYiÓm. RNU×s°Lû[ ©ôõjÕ AúR Gi¦dûL«pAûUdL úYiÓm. úRûYlThPôpé_ó_õVjûR úNôódLÜm. ©\Ï YÏdLÜm.

0.75 I 0.25 Bp YÏdLÜm.

37525

25

75

100

100x

0.25

0.75

0.750.25

=

=

RNU ×s°ûV ùTÚdL, ùTÚdÏ Gi10 BL CÚkRôp, Gi¦dûLdÏYXÕ TdLm JÚ CPm Rs° SLôójRúYiÓm. Gi 100 BL CÚkRôpCWiÓ CPm Rs° ûYdL úYiÓm.AúR Uô§ôõ ùTÚdÏ 1000þdÏm UtßmCúRúTôp Ï±dL úYiÓm. 10 þBpYÏjRôp RNU ×s°ûV JÚ CPmCPÕ TdLm Rs° AûUdLúYiÓm. CÕúY 100 BL CÚkRôp,CWiÓ CPj§tÏ RNU ×s°ûVSLôój§ ûYdL úYiÓm UtßmCûRúV ùRôPWúYiÓm.

ERôWQm

900 ª.Á ¿[Øs[ Tôôõp JqùYôÚ ÕiÓùYhÓYRtÏm 3 ªÁ A§LUôL ûYjÕGÓjÕd ùLôiPôp GjRû] ©uLs¡ûPdÏm? ùTôÚ°p ÁR ¿[m GqY[ÜCÚdÏm?

1 ©u²u ¿[m

= 2.25 + 55.36 + 15.18

= 69.79 ª.Á

Tô¬u ¿[m = 900 ª.Á


22

©u]jûR RNUUôL Uôtß

ERôWQm

• ©u]jûR RNUUôL Uôt\Üm.

I NôRôWQ Øû\«p YÏdLÜm, B]ôp

é_ó_õVjûR (úRûYVô] A[®tÏ) 9Gi¦tÏ (Numerator) ©\Ï AûUdLÜm.

169

=0.5625

• I RNU©u]UôL UôtßL

0.875

0 40 40

56 60

6470008

ÑZp RNU ©u]m (Recurring decimals)

©u]j§p CÚkÕ RNU ©u]j§tÏ UôtßmùTôÝÕ £X ©u]eLû[ N¬Vô] RNU©u]j§tÏ YÏdL Ø¥Ùm. £X ©u]eL°pDÜ Ø¥®pXôUp ùRôPÚm CR]ôp CRtÏÑZp ©u]m Guß ùTVo.

vùPl 1

ùYhPlTP úYi¥V ©u²u Gi¦dûL= X

X Gi¦dûL Es[ ©u²u ¿[m= X x 69.79 ªÁ

vùPl 2

JqùYôÚ ©uàdÏm HtTÓm L¯Ü = 3 ªÁ

L¯Ü x ©u²u Gi¦dûL= 3 x X ªÁ = 3XªÁ

(1) + (2) - I áh¥ Utßm Lm©«u ¿[j§tÏNUuTÓjRÜm.

69.79 X ªÁ + 3 X ªÁ = 900 ªÁ

X (69.79 ªÁ + 3 ªÁ) = 900 ªÁ

X (72.79 ªÁ) = 900 ªÁ

X = 900 ÷ 72.79

12 ©uLs ùNnV CVÛm

CWiPôYRôL

ÁRm Es[ ùTôÚ°u ¿[m.

= Lm©«u ùUôjR ¿[m – 12 ©uL°u¿[m + ùYhÓm ùTôÝÕ HtTÓmL¯ÜLs.

= 900 ªÁ – (12 x 69.79 + 12 x 3) ªÁ

= 900 – (837.48 + 36) ªÁ

= 900 – 873.48

= 26.52 ªÁ

ÁRm Es[ Lm© = 26.52 ªÁ

RNUj§p CÚkÕ ©u]j§tÏ UôtßRp AúRUô§¬ §Úl© ùNnRp

RNUjûR ©u]UôL Uôtß.

ERôWQm

0.375 I ©u]UôL Uôtß

1 I ̧ úZ Ï±dLÜm, AûRj ùRôPokÕ êußCXdLj§tÏ êuß é_ó_õVm Ï±dLÜm.



23

ERôWQm

• UôtßL

a ÑZp RNUm

b ÑZp RNUm

c

CûYLs GiL°u ÁÕ ×s° ûYjÕ ¸úZEs[T¥ GÝRlTÓ¡\Õ.

0.3333 ——> 0.3

0.6666 ——> 0.6

0.14857142 —> 0.14857

LY²dL : ×s°Ls GiLs ÁÕûYdLlTÓ¡\Õ.

ùTô±«Vp Õû\«p LQd¸Ó ùNnÙmùTôÝÕ ùTôÕYôL SôuÏ RNUm YûW RNU×s°Ls ûYlTÕ EiÓ.

LQd¸Ó ùNnVlThP A[ÜL°uU§l©u úRôWôVm (Approximations in M.V.calculations)

M.V.LQd¸ÓL°p SôuÏ RNU CPeLú[úTôÕUô]ûY G²àm TWôU¬l×úYûXL°p CVk§Wj§u TôLeLÞdÏA[ÜLs Ï±dÏm ùTôÝÕ ùTÚmTôÛmêuß RNU CPeLú[ úTôÕUô]RôÏm.

úRôWôVUô] RNUeLû[ GÝÕm Øû\

1.73556 = 1.7356 SôuÏ RNUeLÞdÏ N¬VôL

5.7343 = 5.734 êuß RNUeLÞdÏ N¬VôL

0.9345 = 0.94 CWiÓ RNUeLÞdÏN¬VôL

10,100,1000 B¡VYt\ôp ùTÚdLp UtßmYÏjRp (Multiplication and division by 10,100,1000)

RNUjûR 10 Bp ùTÚdÏRp.

RNU ©u]jûR 10,100,1000 úTôu\ GiL[ôpùTÚdÏm ùTôÝÕ, RNU ×s°Lû[ YXÕTdLj§p ûYdL úYiÓm. ùTÚdLÛdÏHt\Yôß é_ó_õVjûR ûYdL úYiÓm.

• 4.645 x 10 = 46.45 (JÚ CPm)

• 4.645 x 100 = 464.5 (CWiÓ CPm)

• 4.645 x 1000 = 4645 (êuß CPm)

RNUjûR 10 Bp YÏjRp

RNU ©u]jûR 10,100,1000 úTôu\ GiL[ôpYÏdÏm ùTôÝÕ, RNU ×s°ûV CPÕ TdLmSLoj§ ûYdL úYiÓm. YÏjRÛdÏ Ht\Yôßé_ó_õVjûR ûYdL úYiÓm.

ERôWQeLs

• 3.732 ÷ 10 = 0.3732 (JÚ CPm)

• 3.732 ÷ 100 = 0.03732 (CWiÓ CPm)

• 3.732 ÷ 1000 = 0.003732 (êuß CPm)

ERôWQm

• ¸rLiP GiLû[ ©u]eL[ôL ÁiÓmGÝÕL.

453.273

453.273

• ùLôÓdLlThP Gi 0 .386 - - -- dÏ RNUCPj§u ̈ ûX«û] GÝRÜm.

3 - ØRp RNU CPm

8 - CWiPôYÕ RNU CPm

6 - êu\ôYÕ RNU CPm

• ¸rLiP RNUjûR, êuß CPeLÞdÏúRôWôVUôL GÝRÜm.

a 6.9453 ——> 6.945

b 8.7456 ——> 8.746

• ©u]eLû[ RNU ©u]UôL Uôtß

• RNU ©u]jûR ©u]UôL Uôtß

ÑZp RNUm



24

§\]ônÜ T«t£ (Assignment)

1 ¸rLiP RNU GiLû[ ®ôõYôdL Øû\«pGÝÕL.

a 514.726

b 902.524

2 ¸rLiP ®ôõYôdL Øû\«p Es[ RNUGiLû[ RNU ©u]UôL GÝÕL

a

b

3 ¸rLiP RNU ©u]eLû[ NôRôWQ©u]UôL G°V Øû\«p UôtßL

a 0.72

b 5.45

c 3.64

d 2.05

4 ¸rLiP ©u]eLû[ RNU ©u]UôLUôtßL

a

b

c

d

e

f



25

TôdùLh LôpÏúXhPo Utßm ARu TVuTôÓLs T«t£ 1.2.08

L¥]Uô] LQdÏLû[ Ïû\kR úSWj§pTôdùLh LôpÏúXhPo êXm ¾oÜ LôQCVÛm. JÚ NôRôWQ LôpÏúXhPWôp, L¦RNmTkRUô] LQdÏLs ARôYÕ áhPp,L¯jRp, ùTÚdLp Utßm YÏjRpB¡VûYLû[ ¾odLXôm, G²àm®gOô]m Utßm ùRô¯p ÖhT LôpÏúXNàdÏ ®gOô] LôpÏúXhPûWTVuTÓjRXôm.

LôpÏúXhPûW TVuTÓjÕYRtÏ £\l×T«t£ GÕÜm úRûY CpûX. B]ôpLôpÏúXhPo úYûX ùNnÙm ®RjûRúUàYp êXm AdLû\ÙPu T¥jÕ ùR¬kÕùLôsYRu êXm ARu ØÝûUETúVôLjûR TVuTÓj§d ùLôs[Xôm.LôpÏúXhPo ÑVUôL £k§dLôÕ UtßmùNVpTPôÕ, CVdÏTYu ×¬kÕ ùLôiÓLQdÏLû[ ̧ êXm LôpÏúXhPûW N¬VôLCVdL úYiÓm.

LhPûUdLlThP ®[dLeLs (TPm 1)

¸úTôoPô]Õ ARu TWlûT ÑXTUôL×¬kÕdùLôsÞm YûL«p 5 BL ©¬dLlThÓs[Õ.

• úPhPô Gi¼Ã ¸ - Ls

Gih¥¬ ¸-Ls 0 ________ ØRp 9 YûWCÚdÏm.

RNU ×s°«u ¸ .

• ¡°V¬e ¸ - Ls

CkR ¸«p ‘C’ GÝjÕ CÚdÏm

¡°Vo úPôhP≠C CLR

CE

CM MC

áhPp ¸

L¯jRp ¸

ùTÚdLp ¸

YÏjRp ¸

NUUô] ¸, ®ûPûV A±®dÏm ¸=

¡°Vo ùUúUô¬

+

—

x

÷

• @Te`u ̧ (Function keys)

ûT ¸

x YodL êXm ¸

NRÅRm ¸

Ï±ûV Uôtßm ¸

YodLj§u ¸

TWvTWm ¸ (ùW£×úWôdLp ¸)

π

%

+/-

x2

1x

• ¨û]Ü ¸ - Ls (Memory keys)

¥v©ú[ GiLû[ úNªjRp

¥v©ú[ U§lûT ùUúUô¬Ù-Pu áhÓYRtÏ

¥v©ú[ U§lûT ùUúUô¬«pCÚkÕ L¯lTRtÏ

úNªjR U§lùTiLû[ÁiÓm ¥v©ú[«p ùLôiÓYÚRp

M

M+

M-

MR RCL

¡°Vo GuP¬ UhÓm

úUÛm TX úYûXLs ùNnÙm @TeL`]p¸-Ls N«u¥©d LôpÏúXhP¬p AûUdLlThÓs[ûR TPm 2 LôhÓ¡\Õ.


26

ØdúLôQ®Vp ùNVp-TôÓLs UtßmAûPl× Ï±Ls ùNVpTôh¥tLôL

£X ¸ L°p LXo GÝjÕdLs ¸úZApXÕ úUúX AûUkÕ CÚdÏm. LXoGiLû[ TVuTÓjR INV ¸ûVAÝjRÜm. ¥v©ú[«p INVúRôu±V©\Ï ̧ ûV AÝj§]ôp LXoGÝjÕLû[ AÕ C]mLiÓùLôsÞm. ¥v©ú[«p CÚkÕ INVClùTôÝÕ Uû\kÕ®Óm.

CRu êXm ¥v©ú[ GiÔdÏ UPdûL U§l×m LôQXôm Utßm, ¥v©ú[ U§l©tÏ G§o UPdûL GiûQÙm LôQXôm.

¥v©ú[«p ùR¬Ùm ùNqYLúLôBo¥ú]h¥p CÚkÕúTôXôo úLô Bo¥ú]h BLUôtßYRtÏ.

¥v©ú[«p ùR¬Ùm úTôXôoúLô Bo¥ú]h¥p CÚkÕùNqYL úLô Bo¥ú]hÓdÏUôtßYRtÏ.

• ¥v©ú[

Cu×h úPhPô, CûP úSW Ø¥Ü, UtßmLQd¡u ®ûPLs ¥v©ú[«p LôhÓm.

TWl©p AûUdLlThPûYLsJqùYôÚ RVô¬l©Ûm UôßThÓCÚdÏm. EXL A[®p GiLs JÚÏ±l©hP YûL«pRôu AûUdLúYiÓm Guß Ø¥Ü ùNnVlThÓs[Õ. ARuT¥Rôu 10 GiLsùNhPôL AûUdLlTÓ¡\Õ.

Sin Cos Tan ( )

Exp GdvúTô]uh ̧

INV

log INV 10x

INV R–P

INV P–R

= 23.9

®§Ls Utßm ERôWQeLs :

• áhPp : ERôWQm 18.2 + 5.7

• YÏjRp : ERôWQm 18.5/2.5

YÏTÓm GiLû[AÝjRÜm

÷ ¸ûV AÝjRÜm

YÏjRp GiLû[ AÝjRÜm. YÏTÓm Gi T§ÜùNnVlTÓm.

= ̧ ûV AÝjRÜm

+

=

Y¬ûNlT¥ Cu×h ¥v©ú[

18.5

18.5

2.5

7.4

.

.

1 8 5

52

ùTÚdLlTÓm GiLû[AÝjRÜm

x ̧ ûV AÝjRÜm

ùTÚdLp GiLû[AÝjRÜm

= ̧ ûV AÝjRÜm


• ùTÚdLp : ERôWQm 0.47 x 2.47

. 4 7

x

2 . 4 7

=

0.47

0.47

2.47

1.1609

ØRp Y¬ûN Ï±dLÜm

— ̧ ûV AÝjRÜm

L ¯ d Ï m G i L û [AÝjRÜm

= ̧ ûV AÝjRÜm

• L¯dLÜm : ERôWQm 128.8 — 92.9


128.8

128.8

92.9

35.9

1 2 8 . 8

-

9 2 . 9

=

áhÓj ùRôûL«uY¬ûNûV AÝjRÜm

+ ̧ ûV AÝjRÜm

C W i P ô Y Õá h Ó j ù R ô û L « uY¬ûNûV AÝjRÜm

ØRp Y¬ûN T§Ü ùNnVlThÓ CÚdÏm = ¸ûVAÝjRÜm

1 8 . 2

+


5 . 7 5.7

= 23.9

18.2

18.2



27

2.5 AÝjRÜm

x ¸ûV AÝjRÜm

7.2 AÝjRÜm÷ ̧ ûV AÝjRÜm

4.8 I AÝjRÜm

= ̧ ûV AÝjRÜm

¨û]®p ùLôs[Üm:ØRp U§lûT Cu×hùNnYRtÏ Øu©u]j§tÏ ¸úZ Es[úLôhPôp, ¸ûV ùNVp

TÓjR úYiÓm.

1.25 AÝjRÜm

= ̧ ûV AÝjRÜm

1 2 5 1.25.

= 3.0

• ùTÚdLÛm YÏjRÛm :ERôWQm : 2.5x7.2/4.8x1.25


2.52 . 5

x

7 . 2

÷

2.5

7.2

1.8

4.8

3.75

8.4

=

• ùUúUô¬ûV úNªjRp : ERôWQm (2+6)(4+3)


ØRp AûPl× Ï±ûV 2 2ùNVp TÓjR úYiÓm

+ 2

6 6

= 8

ØRp ®ûPûV úNªdLÜm STO , M 8

x or M+

CWiPôYÕ AûPl× 4 4Ï±ûV ùNVpTÓjRúYiÓm + 4

3 3

= 7

x ¸ûV AÝjRÜm x 7

ùUúUô¬ûV §ÚmT RCL or MR 8AûZdLÜm

= ̧ ûV AÝjRÜm = 56


• NRÅRm : ERôWQm 1500 dÏ 12 NR®¡Rm

1500 I ÖûZdLÜm 1 5 0 0 1500

x ¸ûV AÝjRÜm x 1500

12 I ÖûZdLÜm 1 2 12

INV % AÝjRÜm INV % 12

= ¸ûV AÝjRÜm = 180

a

a

a


• YodL êXm : ERôWQm 53 2 ×+

2 I ÖûZdLÜm 2 2

a ̧ ûV AÝjRÜm 2

+ ̧ ûV AÝjRÜm + .

©WôdLh ̧ ûV AÝjRÜm ( .

3 I ÖûZdLÜm 3 3

a ̧ ûV AÝjRÜm .

x ¸ûV AÝjRÜm x .

5 I ÖûZdLÜm 5 5

a ̧ ûV AÝjRÜm .

ê¥V AûPl× ̧ ûV AÝjRÜm ) .

= ̧ ûV AÝjRÜm = 5.2871969

2 + ( 3 x 5 ) = 5.2871969

• ùTôÕYô] UPdûL :ERôWQm Xôd 1.23

1 . 2 3 log = 0.0899051

• UPeÏ : ERôWQm 123 + 302

1 2 3 + 3 0 INV X2 = 1023





28

• LQd¸Ó BWm©dÏm Øu ‘ON’ ¸ûVAÝj§, ¥v©ú[«p ‘0’ ùRôõ¡u\RôGuß TôôódL úYiÓm.

• LôpÏúXhPôõu EhTÏ§Lû[ùRôPdáPôÕ. úYLUôL RhÓYûRR®ôódLÜm. ªLÜm AÝjRUôLAÝjRdáPôÕ

• ùYlT ¨ûX 0° ØRp 40° C YûW«pLôpÏúXhPûW TVuTÓjRÜm.

• B®VôLd á¥V §WYm ARôYÕXôdÏVo, §u]ôó, ùTuûNu B¡VûYLû[d ùLôiÓ, LôpÏúXhPôóTôLeLû[ ÑjRm ùNnVdáPôÕ.

• LôpÏúXhPûW Yû[lTúRôApXÕ¸úZ úTôÓYûR R®odL £\l× LY]mùLôs[Üm.

• CÓl× TôdùLh¥p EuàûPVLôpÏúXhPûW GÓjÕfùNpXdáPôÕ.


1 LôpÏúXhPûW TVuTÓj§ ¸úZEs[ûYLû[ ¾ôóÜ ùNn

a 625 + 3467 + 20 + 341 + 6278 = ______

b 367.4 + 805 + 0.7 + 7.86 + 13.49 = ______

c 0.043 + 1.065 + 13.0 + 34.76 + 42.1 = ______

d 47160 + 1368.4 + 0.1 + 1.6901 + 134.267 =_______


a 24367 — 4385 = ______

b 9.643 — 0.7983 = ______

c 4382.01 — 381.3401 = ______

d 693.42 — 0.0254 = ______

3 LôpÏúXhPûW TVuTÓj§ ¸úZEs[Yt±u U§lûT ùNn

a 23 x 87 = ______

b 1376 x 0.81 = ______

c 678 x 243 = ______

d 0.75 x 0.24 = ______


a 22434 ÷ 3 = ______

b 4131 ÷ 243 = ______

c 469890 ÷ 230 = ______

d 3.026 ÷ 0.89 = ______

5 ¸úZ Es[ûYLÞdÏ ¾ôóÜ LôiL

a = ________

b ________

6 ¸úZ Es[ûYLÞdÏ ¾ôóÜ LôiL

a =−+

8x0.30.52)128)x(384(634

________

b =+−

−−−17.04).10.021)x(28(3.89

2.6)0.0512.2)x(842(389 _________

®hPm (ø) = 782 mmúLôQm (α ) = 136°YhPúLôQlTÏ§«uTWlT[Ü (A) =

°

=360

αx

4

d x π A

2 Ï±l×

TdLm (2a) = 450 ª.Á

TdLm (2b) = 250 ª.Á

¿s YhPj§uÑt\[Ü(c)= _____Á

Ï±l× C = )(2 22 ba +π

7

®hPm (d) = 1.25 ÁL] A[Ü(V) = ______ ùP£ Á3

3πr

3

4V =Ï±l×

9

10

8

¿[m (L) = 1.2 ÁALXm (B) = 0.6 ÁEVWm (H) = 0.5 ÁG@¡u APoj§ = 7.85 ¡.¡/ùP£Á3

¨û\(m) = ______ ¡úXô¡Wôm(¨û\ (m) = V x r )



29

LôpÏúXhPûW TVuTÓj§ ¾oÜ LôÔRp T«t£ 1.2.09

1 ¸úZ Es[Ytû\ RLô ©u]UôL UôtßL

a __________7

21 =

b __________534 =

c __________5

33 =

d __________8

75 =

e _________3

13 =

f ______4

35 =

g __________7

37 =

h __________74

1182 =

2 ¸úZ Es[Ytû\ LXl× GiQôL UôtßL

a __________11

12=

b __________14

36=

c __________10

18=

d __________3

25=

e __________13

84=

f __________21

32=

g __________16

18=

h __________4

75=

3 ®ÓThP GiLû[ ̈ Wl×L

a __________91x

1311

=

b __________x

42

5

3=

c __________98

x

14

9=

4 ÑÚdÏL

a _________60

45=

b __________12

8=

c __________14

12=

d __________72

56=

e __________14

6=

f __________6

14x

4

2x

3

11x

7

5x

4

3=

5 ùTÚdLp

a __________32x5 =

b __________2x43

=

c __________65x

43

=

d __________3x413 =

e __________413x

412 =

f __________416x5 =


30

6 YÏjRp

a _________ 4

3

4

1=÷

b ________ 4

36 =÷

c __________7

2

4

3=÷

d __________46

13 =÷

e ________ =÷7

12

2

15

f _________4

138 ÷

7 ®ÓThP GiLû[ ̈ Wl×L

a x_________12

1

3

2=

b x________121

2414

=

c x_________121

87=

d x_________121

362

=

e x_________121

3652

=

f x_________121

24113 =

g x_________121

43=

h x_________121

67=

8 ¸úZ Es[Ytû\d áhÓL

a _________12

7

4

3=+

b _________4

3

8

7=+

c _________83

54

53

=++

d _________973

1271

416 =++

9 L¯jRp

a _________52

54

=−

b _________43

65

=−

10 ÑÚdÏL

a _________16

11

3

1

8

3

7

62 =−−−

b ________86

5

7

22 =+−

c _________2

12

4

31

5

3

9

73 =+−+−

11 RLô ©u]UôL ùY°lTÓjÕL

a4

35

b64

53

c12

51

12 LXl× GiQôLúYô (A ) ØÝGiQôLúYô Ïû\dLÜm.

a4

163

b4

12

c60

144

13 Ïû\kRThN A[YôL ÑÚdLd LôhPÜm

a64

12

b48

12

c60

144



31

14 RNUeL°u áhPp

a 4.56 + 32.075 + 256.6245 + 15.0358

b 462.492 + 725.526 + 309.345 + 626.602

15 RNUd L¯jRp

a 612.5200 – 9.6479

b 573.9246 – 215.6000

c 968.325 – 16.482

d 5735.4273 – 364.2342

16 áhPp Utßm L¯jRp

a 56.725 + 48.258 – 32.564

b 16.45 + 124.56 + 62.7 - 3.243

17 RUNeL°u ùTÚdLp

a By 10,100,1000

i 3.754

ii 8.964 x 100

iii 2.3786 x 1000

iv 0.005 x 1000

b ØÝ GiQôp ùTÚdÏRp

i 8.4 x 7

ii 56.72 x 8

c Utù\ôÚ RNUjRôp ùTÚdÏRp(LôpÏúXhPo ETúVô¡dLÜm)

i 15.64 x 7.68

ii 2.642 x 1.562

18 ¸úZ Es[Ytû\ YÏdLÜm

a25

62.5

b9

14.4

c10

64.56

d100

0.42

e1000

48.356

f15

25.5

19 YÏjRp

a1.2

16.8

b1.2

1.68

c1.2

0.168

d1.1

1.54

e1.6

27.2

f 31.5 ÷ 10.5

g 1.54 ÷ 1.1

h 4.41 ÷ 2.1

20 ©u]jûR RNU©u]UôL Uôt\Üm

i 18

5

ii25

12

21 U§lûTd Lôi

20.5 x 40 ÷ 10.25 + 18.50

22

23

24

25

A = 12.613 ªÁX = _________ ªÁ.

X = __________ ªÁ.

X = __________ªÁ.

B = __________ªÁ.



32

YodLm Utßm YodLêXm T«t£ 1.3.10

a A¥lTûP Gi (Basic number)

2 Ï± Gi (exponent)

YôódL êXj§u AûPVô[m

a2 þu YodLêXm (A) YodLj§u

YodLêXm a2 þu êXm.

YodL Gi (Square number)JÚ YodL Gi GuTÕ JÚ GiRuû]jRôú] AúR GiQôp ùTÚd¡dùLôsYÕ.

A¥lTûP Gi x A¥lTûP Gi = YodLGi

a x a = a2

4 x 4 = 42 = 16

©ôõjRp (Splitting up)JÚ NÕW TWlT[ûY £±V TWl×L[ôL ©ôõdLCVÛm. ªLl ùTôõV NÕWm 36, 16 ùTôõVTWl©u êXUôL LhPûUdLlThÓs[Õ,C§p Es[ £±V NÕWm 4 Utßm 8Gi¦dûL«Ûs[ 2 ùNqYLeLs.

ùTôõV NÕWm 4 x 4 = 16 a2

CWiÓ ùNqYLm 2 x 4 x 2 = 16 2ab

£±V NÕWm 2 x 2 = 4 b2

£±V TWl©u áhÓjùRôûL = 36 = a2 + 2ab + b2

Ø¥Ü: YôódL êXm LiÓ©¥dL YodLGiLû[ Sôm ©ôõdL úYiÓm.

YôódL êXjûR ©¬jùRÓjRÛdLô]ùNnØû\

• CWiÓ GiL°u ùRôÏl©tÏ RNU×s°ûV YXÕ TdLm Utßm CPÕ TdLmûYdL úYiÓm. Ød¡VUô] Ï±ÂûP

Ï±dLÜm.

• ØRp ùRôÏl©tÏ YôódL êXm LôiL.®j§VôNjûR LiÓ©¥jÕ, AÓjRùRôÏl©tÏ ùLôiÓ YWÜm.

• êXjûR (Root) 2 Bp ùTÚdLÜm UtßmYÏjRp Øû\«p Yô ódL êXjûRLôQXôm.

• GiLû[ Ï±dLÜm ClT¥VôL YÏTÓmGiQôp ùTÚdLÜm.

ÁRm CÚkRôp, CûRúV §ÚmTÜm ùNnVÜm.

JÚ GiûQ AúR GiQôpùTÚd¡]ôp = YôódLm

number basic number Square =

ERôWQm

ôõùYh¥u ÏßdÏ ùYhÓ TWlT[Ü 3.46ùN.Á2. Õû[«u ®hPjûR LQd¸ÓùNnVÜm.

ôõùYh¥u ÏßdÏ ùYhÓ, Õû[«u ÏßdÏùYhÓdÏf NUm.

d1 þI LiÓ©¥dL

ùLôÓdLlThP TWlT[Ü = 3.46 cm2

TWlT[Ü = 0.785 x d2 (ãj§Wm)3.46 cm2 = d1

2 x 0.785

21mm (or) cm 2.1 d

cm 0.7853.46 d

0.785cm 3.46 d

22

=

=

=


33

LôpÏúXhPûW TVuTÓj§ G°V LQdÏLs ùNnRp T«t£ 1.3.11

1 a .

b .

c .

d .

2 TWlT[Ü (A) = 2025ª.Á2

a = ª.Á

6 TWlT[Ü (A) =807.77 ùN.Á2

Es®hPm (d) =140 ª.Á

ùY° ®hPm (D)= ª.Á

3 T W l T [ Ü ( A ) =176.715 ª.Á2

d= ª.Á

4 TWlT[Ü (A) =65031 ª.Á2

£±V ®hPm (d) =140 ª.Á

ùTôõV ®hPm (D)= ª.Á

5 ¿[m (I) = 58 ùN.Á

ALXm (b) = 45ùN.Á

TWlT[Ü (A1)=TWlT[Ü (A2)

a = ùN.Á

7 TdLm (a) x TdLm(a) = 543169

TdLm (a) =ª.Á

8 d : l = 1:1.5

TWlT[Ü A = 73.5ª.Á2

d (®hPm) =__ª.Á

9 A§L¬dLlThPTWl×A = 12.7%

A = 360 mm2

d (®hPm) =__ª.Á

(d = A§L¬dLlThPT W l © ] ô pHtThP ®hPm)


34

©RôLWv úRt\jûR TVuTÓj§ ùNnVlThP LQdÏLsT«t£ 1.3.12

1 TdLm ‘AC’- I Lôi AB = 15 ùNÁ, BC = 25ùNÁ.

AC2 = AB2 + BC2

= 152 + 252

= 225 + 625 = 850

AC = 850 = 29.155 cm

2 TdLm ‘BC’- I Lôi AB = 10 ùNÁ, AC = 30ùNÁ.

AC2 = AB2 + BC2

302 = 102 + BC2

900 = 100 + BC2

BC2 = 900 - 100 = 800

BC = 28.284 cm

3 TdLm ‘AB’- I Lôi BC = 20 ùNÁ, AC = 35ùNÁ.

AC2 = AB2 + BC2

352 = AB2 + 202

1225 = AB + 400

AB2 = 1225 - 400 = 825

AB = 28.72 cm

4 TdLm ‘BC’- «u U§lûTd Lôi AB = 8 ùNÁ,AC = 24 ùNÁ.

AC2 = AB2 + BC2

242 = 82 + BC2

576 = 64 + BC2

BC2 = 576 - 64 = 512

BC = 572 = 22.63 cm

5 TdLm ‘AC’- «u U§lûTd Lôi AB = 6.45ùNÁ, BC = 8.52 ùNÁ.

AC2 = AB2 + BC2

AC2 = 6.452 + 8.522

AC2 = 41.60 + 72.59

= 114.19

AC = 114.19 = 10.69 cm

6 TdLm ‘AB’- «u U§lûTd Lôi BC = 3.26ùNÁ, AC = 8.24 ùNÁ.

AC2 = AB2 + BC2

8.242= AB2 + 3.262

67.9 = AB + 10.63

AB2 = 67.9 - 10.63

= 57.27

AB = 57.27 = 7.57 cm

7 TdLm ‘AB’ - «u U§lûTd Lôi AC = 12.5ùNÁ, BC = 8.5 ùNÁ.

AC2 = AB2 + BC2

12.52 = AB2 + 8.52

156.25 = AB + 72.25

AB2 = 156.25 - 72.25

= 84

AB = 84 = 9.17 cm


• JÚ ùNeúLôQ ØdúLôQj§p TdLm AC =12.5 ùNÁ Utßm TdLm BC = 7.5 ùNÁ G²pTdLm ‘AB’ - u U§lûTd Lôi.

• JÚ ùNeúLôQ ØdúLôQj§p TdLm AB =6.5 ùNÁ Utßm TdLm BC = 4.5 ùNÁ G²pTdLm ‘AC’- u U§lûTd Lôi.

• JÚ ùNeúLôQ ØdúLôQj§p TdLm AC =14.5 ùNÁ Utßm TdLm AB = 10.5 ùNÁ G²pTdLm ‘BC’- u U§lûTd Lôi.

• JÚ ùNeúLôQ ØdúLôQj§p TdLm AB =7 ùNÁ Utßm TdLm BC = 5 ùNÁ G²pTdLm ‘AC’- u U§lûTd Lôi.

• JÚ ùNeúLôQ ØdúLôQj§p TdLm AC =13.25 ùNÁ Utßm TdLm AB = 8.75 ùNÁG²p TdLm ‘BC’- u U§lûTd Lôi.


35

®¡Rm Utßm ®¡R NUm T«t£ 1.4.13

®¡Rm (Ratio)

A±ØLm

CWiÓ Wô£L°u Kôõ] A[ÜLû[Jl©ÓYRtÏ ®¡Rm Guß ùTVôó. CÕ©u]j§p ùY°lTÓjRlTÓ¡\Õ.

ùY°lTÓjÕRp (Expression)

a, b Gu\ CWiÓ Wô£Ls Kôõ] A[ÜLs

ùLôiPÕ. b

a ApXÕ a:b ApXÕ a ÷ b ApXÕ

a in b GuTÕ ®¡Rm

®¡Rm GlùTôÝÕm Ïû\kR GiL[ôLÏû\dLlTÓm

ERôWQm

®¡R NUm (Proportion)

CWiÓ ®¡ReLÞm NUUôL CÚdÏm, a : bGuTÕ ®¡Rm Utßm c: d GuTÕ Utù\ôÚ®¡Rm. CWiÓ ®¡ReLÞm NUm.

©\Ï,

a :b :: c : d or

ERôWQm

250 : 2000 :: 1 : 8

®¡R NUeL°uA¥lTûPLs (Proportionfundamentals)

G²p ©\Ï

• ad = bc

•

•

•c

dc

b

ba +=

+ Utßm

c

dc

a

ba +=

+

•

•

3:4::6:8 or

• 3 x 8 = 6 x 4

•

•

•

•

• 43

129

8 46 3

==++

• ®¡RmþCWiÓ Wô£L°u Kôõ]A[ÜLû[ Jl©ÓYÕ ®¡RmBÏm.

• ®¡R NUmþCWiÓ ®¡ReLÞmNUUôL CÚlTÕ ®¡RNUm BÏm.

ERôWQm

• 1:20 vúLÛdÏ, 800 x 1400 ª.Á G@Ï RLÓYûWVlTÓ¡\Õ. AkR RLh¥u ¿[mGqY[Ü? (TPmþ1)

Ïû\dLlThP ®¡Rm .

800 þp CÚkÕ Ïû\dLlThP B = 800 x = 40

ª.Á

Ïû\dLlThP ¿[m ( L) 1400 x = 70 ª.Á


36

• ¡Vôó ¥WôuªNu²p, ùTôõV ¡Vôõp Es[TtL°u Gi¦dûL LiÓ©¥. (TPm 2)

úYLj§u ®¡Rm = 400 : 300

TtL°u ®¡Rm = 24:T

TtLs

A:B= 2:3 Utßm B:C=4:5 G²p A:B:C= _________ -- I LôiL,

A:B = 2:3

B:C = 4:5

A:B = 8 :12 (®¡Rm 2:3, 4- Bp ùTÚdLlThÓs[Õ.)

B:C = 12:15 (®¡Rm 4:5, 3 Bp ùTÚdLlThÓs[Õ.)

∴ A:B:C = 8:12:15


5 D : d = 1.75: 1ùTôõV ®hPm (D)= 35 ª.Á£±V ®hPm (d) =______ª.Á

6 a:s = 5:1

s = 1.5 ª.Á

a =______ ª.Á

7 A:B=9:12

B:C=8:10

G²p A:B:C=___________

8 A:B=5:6

B:C=3:4

G²p A:B:C= ___________

9 A:55=9:11

A = __________

10 15:9.3=40:x

x = ___________

1 l1 : l2 = 2:3¿[m (L) = 2.75ÁhPôóLsl1 = ______ÁhPôóLsl2 = ______ÁhPôóLs

2 `ôl¥u ®hPmd:`ôl¥u ¿[m(l)=2:7®hPm (d) = 40 ª.Á¿[m (L) = ______ª.Á

3 ® h P m : ¿ [ m(D:L)=1:10¿[m (L)=150 ª.Á®hPm (D) =______ª.Á

4

¿[m (l)=140ª.Áh = ________ ª.Á



37

úSôó Uô\p Utßm G§ôó Uô\p T«t£ 1.4.14

®¡R NUm (Proportion)

®YWm (Description)

CWiÓ ®¡RØm JußdùLôuß NUUôLCÚdÏm, a:b GuTÕ JÚ ®¡Rm Utßm c:dGuTÕ Utù\ôÚ ®¡Rm. CWiÓ ®¡RØmNUUô]ûY. G²p

a : b::c : d ApXÕ ERôWQm 250 : 2000::1 : 8

êuß ®§Ls (Rule of three)

LQd¸Ó ùNnV êuß vùPlLs

• ®YWm (Statement)

• JÚYôó (Single)

• ùTÚdLp (Multiple)

G§ôóUô\p ApXÕ RûX ̧ r ®¡Rj§pUôßRp (Indirect or inverse proportion)

Ju±u A[Ü A§LôõdÏmùTôÝÕUtù\ôu±u A[Ü Ïû\Ùm. Ju±u A[ÜÏû\kRôp Utù\ôu±u A[Ü A§LôõdÏm.CÕ G§ôó Uô\p G]lTÓm. (TPm 2)

úSôó Uô\p (Direct proportion)

JÚ Wô£ JÚ ®¡Rj§p UôßmúTôÕ AúRôÓùRôPôó×ûPV Utù\ôÚ Wô£Ùm AúR®¡Rj§p UôßYúR úSôóUô\p G]lTÓm.(TPm 1)

ERôWQm

SôuÏ LûPNp ©¥lTYôóLs 300 ìTôn NmTô§d¡u\]ôó. CÕúY 6 LûPNp ©¥lTYôóLs GqY[Ü NmTô§lTôôóLs.

®YWm4 Pôó]ôóLs = ìTôn 300

JÚYôó

1 Pôó]ôó = ìTôn 75

ùTÚdLÜm 6 Pôó]ôóLs= 75 x 6 = 450 ìTôn

Ø¥Ü - A§LUô]ôp A§LôõdÏm

ERôWQm

SôuÏ Pôó]ôóLs JÚ úYûXûV 300 U¦úSWj§p Ø¥d¡u\]ôó CúR úYûXûV BßPôó]ôóLs ùNnÕ Ø¥dL GqY[Ü úSWmúRûYlTÓm?

êuß ¨ûXL°p ¾ôóÜ ùNnVlTÓm:

®YWm

4 Pôó]ôóLs GÓjÕdùLôiP úSWm = 300 U¦

JÚYo

1 Pôó]ôó GÓjÕd ùLôsÞm úSWm= 300 x 4 =1200 U¦úSWm

ùTÚdLÜm

6 turners = = 200 U¦úSWm

Ø¥Ü - A§LUô]ôp Ïû\Ùm

úSôóUô\p Utßm G§ôóUô\p CWiÓmLXkR LQdÏLs (Problem involving both)

ERôWQm

20 ÕiÓLû[ RVôôõdL CWiÓ Pôó]ôóLÞdÏêuß SôhLs úRûYlTÓ¡\Õ. BßPôó]ôóLs 30 ÕiÓLû[j RVôôõdL GjRû]SôhLs úRûY?


38

ØR≠p BWm©lTÕ

2 Pôó]ôóLs, 20 ÕiÓLs = 3 SôhLs

6 Pôó]ôóLs, 30 ÕiÓLs = GjRû] SôhLsúRûY

ØRp vùPl (TPm 3)

®TWmPo]oLs 20 ÕiÓLs ùNnV = 3 SôhLs

1 Po]o 20 ÕiÓLs ùNnV = 3 x 2 = 6 SôhLs

6 Po]oLs 20 ÕiÓLs ùNnV ùTÚdÏL

= = 1 Sôs

G°ûUVô] ®¡RNUm (Simple proportion)

• ®¡RNUm

CWiÓ ®¡ReLÞdÏ CûPúVVô] NU¨ûXBÏm.

ERôWQeLs

• JÚ Yi¥ûV CVdL Sôs JußdÏ 30≠hPo ùThúWôp úRûYlTÓ¡\Õ. 6Yi¥Lû[ CúR ̈ ûX«p CVdL GqY[ÜùThúWôp úRûYlTÓm.

JÚ Yi¥dÏ TVuTÓj§V ùThúWôp = SôsJußdÏ 30 ≠hPoLs

CqYôß 6 Yi¥Ls TVuTÓj§]ôp =

BßUPeÏ úRûYlTÓm = 6 x 30 = 180 ≠hPo/Sôs.

• 4 Yi¥Ls CVeÏYRtÏ Sôs JußdÏ120 úLXu ùThúWôp úRûYlTÓ¡\Õ.CúR ̈ ûX«p 12 Yi¥Ls CVeÏYRtÏGqY[Ü úLXu ùThúWôp úRûYlTÓm.

4 Yi¥Ls JÚ Sôû[dÏ TVuTÓj§VùThúWôp 120 úLXu.

@ JÚ Yi¥ TVuTÓj§V ùThúWôp =

30 úLXu/Sôs.

@ 12 Yi¥Ls TVuTÓj§]ôp 12 x 30 = 360úLXu/Sôs.

CWiÓ ERôWQeLÞm G°ûUVô]®¡RNUm BÏm. Hù]u\ôp, CWiÓA[ÜLs UhÓúU TVuTÓjRlThPÕ Utßm CWiÓ ®¡Rj§ÛmSôhLs ùTôÕYôL Es[].

LXl× Utßm RûX ¸r ®¡R NUuLs(Compound and inverse proporions)

• LXl× ®¡R NUuLs.

ERôWQm

6 Yi¥Lû[ 5 ©hPoLs TÝÕ TôodL 21SôhLs ©¥jRÕ G²p 8 Yi¥Lû[ 7©hPoLs TÝÕ TôodL GjRû] SôhLsBÏm. (JqùYôÚ Yi¥dÏm TÝÕ TôodÏmúSWm ¨ûXVôL ùLôsL)

C§p úSoUô\p Utßm G§oUô\pTVuTÓjRlThÓs[Õ.

• JÚ ©hPo JÚ Yi¥ûV JÚ Sô°p TÝÕTôodL úRûYVô] úSWm. (Ïß¡V úSWm).

RûX¸r ®¡Rm -A§LUô]ôpÏû\Ùm.

CWiPôm vùPl (TPm 4)

®TWm: 6 Po]oLs 20 ÕiÓLs ùNnV = 1Sôs

JÚYo: 6 Po]oLs 1 ÕiÓ ùNnV =

Sôs

ùTÚdL: 6 Po]oLs 30 ÕiÓLs ùNnV= x 30 = 1.5 SôhLs.

úSo®¡Rm-A§LUô]ôp A§L¬dÏm.

LQdÏLû[ ¾oÜ ùNnV, ØR≠p®TWeLû[ GÝRÜm, ARu ©\ÏJÚYo Utßm ùTÚdLÜm,®¡ReL°u YûLûVl ùTôÚjÕ¾oUô²dLÜm.

A±ØLm

úUôhPôo YôL]eLÞdÏ LQd¸ÓùNnYRtLô] A¥lTûP ®¡RôNôWeLs ̧ úZ®Y¬dLlThÓs[Õ.



39

• A[ÜLû[ (GjRû] SôhLs GuTÕ)LûP£«p GÓjÕd ùLôs[Xôm. Hù]²pAÕ ®ûPdLô] úRûYVôÏm.

®ûP; 7 ©hPoLs 8 Yi¥Lû[ 20 SôhL°pTÝÕTôolTôoLs.

SôhLs

RûX¸r ®¡Rm (Inverse proportion)

£X NUVeL°p ®¡ReLû[ RûX¸ZôL GÓdLúYi¥ CÚdÏm.

ERôWQeLs

• JÚ Tm×, G¬ùTôÚs ùRôh¥ûV ¨WlTGÓjÕdùLôsÞm úSWm 12 ¨ªPeLs.CÕúY CWiÓ Tm×Lû[ TVuTÓj§]ôpTô§ úSWj§p ¨WlTXôm.

úSWm CWiÓ UPeLôL BLd áPôÕ.

• CWiÓ Tml×Ls JÚ ùRôh¥ûV¨Wl×YRtÏ 30 ̈ ªPeLs úRûYlTÓ¡\Õ.CúR Uô§¬Vô] 6 Tm×Ls ùRôh¥ûV¨WlT GqY[Ü úSWm úRûYlTÓm.

®ûP ; 6 Tm×Ls GÓjÕdùLôiP

úSWm = ¨ªPm

G¬Rp NUuTôh¥p A[ÜL°u ®¡Rm(Proportional parts in combustion equation)

A±ØLm

A[ÜL°u ®¡Rm, G¬ùTôÚs G¬ÙmØû\dÏ JÚ Ød¡VUô] LôW¦VôÏm. G¬RpSûPùTßm ùTôÝÕ ¸rLiPûYLsSûPùTß¡u\].

G¬ùTôÚs ûahúWô LôoTu ùTôÚ[ôÏm.G¬YRtÏ úRûYVô] Lôtß Y° UiPXj§pCÚkÕ ¡ûPd¡u\Õ, A§p Bd£_u UtßmûShW_u Es[Õ. G¬ùTôÚs G¬ÙmùTôÝÕ ¸rLiP úY§«Vp Uôt\eLsHtTÓ¡u\].

• LôoTu Bd£_ú]ôÓ úNokÕ G¬ÙmùTôÝÕ Co Utßm Co2 BL Uôß¡\Õ.

(LôoTu úUô]dûNPôLÜm LôoTu ûPBdûNPôLÜm Uôß¡\Õ.)

• ûahW_u Bd£_ú]ôÓ G¬Ùm ùTôÝÕAÕ Ri¦WôL Uôß¡\Õ. (H2O)

• NpTo Bd£_ú]ôÓ G¬Ùm ùTôÝÕ AÕ

NpToûP BdûNPôL Uôß¡\Õ.

• ûShW_u JÚ UkRUô] YôÙ. AÕG¬YRtÏ ÕûQ ×¬Y§pûX.

JÚ lb ùTôÚ°p TÏ§«u ®¡RjûRA±Ùm Øû\

ClùTôÝÕ LiÓ©¥dL úYi¥VÕ.

• JÚ lb/kg Ri½¬p Bd£_u UtßmûahW_u ®¡RjûR LôÔRp.

• JÚ lb/kg G¬ùTôÚ°p ûahW_u UtßmLôoT²u ®¡RjûR LôÔRp.

ERôWQeLs

• H2O. GuTÕ Ri½¬u úY§Vp ãj§WmBÏm. CRu ùTôÚs CWiÓ AÔdLsùLôiP ûahW_u Utßm JÚ AÔdLsùLôiP Bd£_²u LXûYLs úNokÕJÚ Uô≠dëp Ri½WôL Uôß¡\Õ.Bd£_u AÔ®u GûP ûahW_²uGûPûVl úTôp 16 UPeÏ A§LùU²pJÚ ¡úXô Ri½¬p ARu ®¡RjûRLiÓ©¥.

¾oÜ (Solution)

Ri½¬p TôLeL°u GûP ¸úZùLôÓdLlThÓs[Õ.

• Bd£_u = 16/2 = 8 ¡úXô

• ûahW_u = 1/1 = 1 ¡úXô

• ùUôjRm = 8+1= 9 ¡úXô

• ûahúWô LôoTu G¬ùTôÚ°u ãj§WmC6H14 BÏm. G¬ùTôÚ°u JÚ Uô≠dëp, 6LôoTu AÔdLs Utßm 14 ûahW_uAÔdLs Guß LôhÓ¡\Õ. ûahW_uAÔ GûPûVl úTôp LôoTu AÔ®uGûPVô]Õ 12 UPeÏ G²p, JÚ ¡úXôG¬ùTôÚ°p Es[ ûahW_u UtßmLôoTu ®¡RjûR LiÓ©¥.

¾oÜ (Solution)

LôoT²u TeÏ GûP«p = 6 x 12 = 72ûahW_u TeÏ GûP«p = 14.

ùUôjR TôLeLs = 72 + 14 = 86.

LôoT²u GûP = 72/86 = 0.8372 ¡úXô

ûahW_²u GûP 14/86 = 0.1628 ¡úXô



40

®¡Rm Utßm ®¡RNUm

G¬YRtÏ úRûYVô] Lôt±u ®¡R A[Ü.

G¬ùTôÚs ØÝûUVôL G¬YRtÏ úRûYVô]Lôt±u ¨û\, ¸rLiP LôW¦Lû[lùTôÚjRÕ. CRtÏ Lôtß G¬ùTôÚs ®¡RmGuß ùTVo.

• – LôoTu, ûahW_u, NpTo B¡VûYBd£_àPu G¬dLlTÓ¡\Õ.

– G¬YRtÏ úRûYVô] Lôt±u A[ûY(GûP«p) LiÓ ©¥jÕ ARu êXmúRûYlTÓm A[®tÏ Bd£_uùNÛjÕlTÓ¡\Õ.

• – 1 ¡úXô LôoTu ØÝûUVôL G¬YRtÏ

= ¡úXô Bd£_u úRûY.

– 1 ¡úXô ûahW_u ØÝûUVôL G¬YRtÏ= 8 ¡úXô Bd£_u úRûY

– 1 ¡úXô NpTo ØÝûUVôL G¬YRtÏ = 1¡úXô Bd£_u úRûY.

• ØÝûUVôL G¬YRtÏ úRûYVô] ̈ û\ûVLiÓ©¥dÏm ãj§Wm

Lôt±p, Bd£_u 23% Utßm ûahW_u77% LXkÕs[Õ.

Lôt±u ̈ û\ = Bd£_u ̈ û\ x JqùYôÚêXlùTôÚÞm.

LôoTu ¡úXô Lôtß

ûahW_u 34.823

1008 =×= ¡úXô Lôtß

NpTo 4.3523

1001 =×= ¡úXô Lôtß

ùUôjRm(Total) 50.75 ¡úXô

CVk§Wj§p TVuTÓjÕm 1 ¡úXôG¬ùTôÚÞdÏ 50 .75 ¡úXô LôtßùNÛjRlTP úYiÓm.

G¬lTRtÏ 50.7 ¡úXô Lôtû\ ®PA§LUôL úRûYlTPôÕ.

LmTvPu NUuTôÓ LQdÏUôQYodÏ ªL A§LUô]A[YôÏm. Hù]²p C§púY§«Vp, CVt©Vp êXm TpúYßêXLeL°u ®¡RjûR LQd¸ÓùNnVúYiÓm.


1 ¿[m = 6.1 ÁhPoGûP = 32 kgfCúR Nô]≠u(channel) 1 ÁhPo¿ [ j § t L ô ]GûP = _______ kgf

2 £±V ®hPmd1 = 120 ªÁùT¬V ®hPmd2 = 720 ªÁ£±V ®hPj§un1 = 1200 rpmùT¬V ®hPj§un2 = ______ rpm

3 Z1 = 42 T

n1 = 96 rpm

n2 = 224 rpm

Z2 = _______ T

4 ám©u ®hPmD = 50 ªÁám©u EVWmH = 80 ªÁ¿ d L l T h Pám©u EVWmh = 36 ªÁ¿ d L l T h Pám©u ®hPmd = ______ ªÁ

5 JÚ ùUdLô²d 8 Gk§WeLû[ 3 SôhL°pANm©°e ùNn¡\ôo. 60 Gk§WeLû[ANm©°e ùNnYRtÏ GjRû] SôhLsBÏm.

6 BhúPô `ôl©p Es[ ¡ûWu¥e ÅpJÚ ¨ªPj§tÏ 1000 Ñtß Ñtß¡u\ÕUtßm ¥ûWYu ×p≠ (driven pulley)«u®hPm 200 ªÁ. ¥ûW®e ×p≠«u(drivingpulley) ®hPm 150 ¡.Á G²p ¥ûW®e×p≠«u rpm LiÓ©¥dLÜm.



41

7 YôL]j§p ¡Vo AûUl©p ¸rLiPEiûULs LiÓ©¥dLlThP] 180 ªÁ®hPm Es[ ¡Vo 60 ªÁ ®hPm Es[¡VÚPu Cû]dLlThÓs[Õ. C§pùT¬V ¡Vo JÚ ¨ªPj§tÏ 60 ÑtßÑtß¡\Õ Gu\ôp. £±V ¡V¬u rpm ILiÓ ©¥..

8 JÚ YôL]m NmTkRlThP úYûXûV 5ùUdLô²dÏLs 4 SôhL°p Ø¥jÕ®hPôoLs G²p 3 ùUdLô²dÏLsGjRû] SôhL°p Ø¥lTôoLs.

9 JÚ YôL]j§p ¡VûW AûUdÏm ùTôÝÕTtL°u Gi¦dûL 26 ùLôiP ¡Vo 52TtLs ùLôiP ¡VÚPuCûQdLlTÓ¡\Õ. 52 TtLû[ ùLôiP¡V¬u ®hPm 200 ªÁ G²p 26 TtLû[ùLôiP ¡V¬u ®hPjûRLiÓ©¥dLÜm.

10 CWiÓ YôhPo Tm×Ls ùRôh¥ûV¨WlT 45 ̈ ªPm B¡\Õ. AúR Uô§¬Vô]4 YôhPo Tm×Ls TVu TÓj§]ôp,ùRôh¥«p Ri½ûW ¨WlT GqY[ÜúSWm BÏm.

11 ùTph ×p≠ CVdLj§p 12 ùN Á ®hPmEs[ ¥ûW®e ×p≠ JÚ ¨ªP§tÏ 360Ñtß Ñtß¡\Õ. G²p 20 ùN Á ®hPØs[¥ûWYu ×p≠«u rpm I LiÓ©¥

12 JÚ ¡Vo TôdûN TÝÕ TôolTRtÏ 12ùUdLô²dLÞdÏ 5 SôhLsúRûYlTÓ¡\Õ G²p B]ôp¡ûPdLdá¥V 7 ùUdLô²dÏLû[ ûYjÕTÝÕ TôodL GjRû] SôhLs BÏm.

13 ¸r LiPûYLÞdÏ NôRôWQ ®¡RmLôiL

a 45 ÷ 60 b 40 ûTNô ÷ ìTôn 4.00

c d 4°C ÷ 100°C

14 Lôtß 22% Bd£_u Utßm 78% ûShW_u¨û\ ùLôiPÕ. G¬ùTôÚs JÚ AXÏØÝûUVôL G¬YRtÏ úRûYVô] Lôt±uGûPûV LQd¸Ó ùNn. (G¬Y§pØd¡VUôL LôoTu, ûahW_u UtßmNpToLs TeÏ Y¡d¡\Õ).

Ï±l×: ¸úZ úPhPô ùLôÓdLlThÓs[Õ(LQdûL ¾oÜ ùNn)

a 1 ¡úXô LôoTàdÏ úRûY 32

2 ¡úXô

Bd£_u.

b 1 ¡úXô ûahW_àdÏ úRûY 8 ¡úXôBd£_u.

c 1 ¡úXô NpTÚdÏ úRûY 1 ¡úXôBd£_u.

15 ûa¥úWô LôoTu G¬ùTôÚ°uêXôRôWm C7H14. CkR G¬ùTôÚ°uJqùYôÚ Uô≠dë≠p, 7 AÔ LôoTàm,Utßm 19 AÔ ûahW_àm CÚdÏm.C§p LôoTu AÔ®u GûP ûahW_uAÔûY ®P 12 UPeÏ A§Lm G²p JÚ¡úXô G¬ùTôÚ°p CÚkÕ ûahW_uUtßm LôoT²u ®¡RjûR LiÓ©¥.

16 ìTôn 20,000/ U§l× EûPV YôL]m, AÕì 150/ dÏ LôlÀÓ ùNnVlThÓs[Õ. CúRA¥lûP«p 24,000/ ìTôn U§l×s[YôL]jûR 1 YÚPm 3 UôRj§tÏ LôlÀÓùNnRôp LôlÀÓ ùRôûL GqY[ÜCÚdÏm. (LômTÜiÓ ®¡Rm).

20 ª.Á

4 ÁhPo



42

NRÅRm T«t£ 1.5.15

NRÅRm (Percentage)

NRÅRm GuTÕ JÚ YûLVô] ©u]m. CRuTÏ§ GlùTôÝÕm 100 BL CÚdÏmNRÅRj§u Ï±ÂÓ% Gi¦tÏ ©\ÏCdÏ±ûV TVuTÓjR úYiÓm. ERôWQUôL

= 16%.

CÕ RNU Y¥Yj§p, 0.16. NRÅRd LQd¸Ómêuß ®§Lû[ Es[Pd¡VÕùLôÓdLlThP úPhPô, AXÏ, Utßm ©\ÏùTÚdÏRp CÕRôu ®ûP LôÔYRtLô]LQd¸Ó Øû\VôÏm. (TPm 1)

Ø¥Ü

C§p TVuTÓjRlThP êuß vùPlLs

ØRp vùPl: ãr¨ûXûV ®[dÏRp(CÚlTûR ûYjÕ ùNnYÕ)

CWiPôm vùPl: AXÏLû[ Ø¥Ü ùNn

êu\ôm vùPl: ùTÚdLp BWm©dLÜm.

ùLôÓdLlThP úPhPôûYTÏjRônÜ ùNnÕ, ®ûPûV AXÏêXUôL LiÓ©¥dLÜm.

ERôWQm (Example)

JÚ ©hPo ©¥jRmúTôL Åh¥tÏ GÓjÕfùNpÛm UôRNmT[m ì 984.50 AYÚûPVNmT[j§p 24%, ©¥jRm ùNnVlTÓ¡\ÕG²p AYÚûPV ùUôjR NmT[m GqY[Ü?(TPm 3)

ERôWQm (Examples)

JÚ v¼p LRÜ RVô¬dL 3.6 N.ÁhPo CÓùTôÚs úRûYlTÓ¡\Õ Utßm C§pHtTÓm úNRôWm 0.18 N.ÁhPo G²púNRôWj§u NRÅR U§l©û] (TPm 2)LiÓ©¥.

êuß vùPl êXm ¾ôóÜ LôQlTÓ¡\Õ

vúPhùUih: (Statement)

LR®u TWlT[Ü (A) = 3.6 Á2 = 100 %.

úNRôWm = 0.18 Á2

JÚYo: 3.6100

1 Á2

ùTÚdLp: for 0.18 Á2= 3.6100

x 0.18.

L¯Ü = 5%.

ùUôjR NmT[m 100%

©¥jRm 24%

ÅhÓdÏ GÓjÕf ùNpÛm NmT[m 76%

100 ìTôn NmT[j§p AYôó ÅhÓdÏ GÓjÕfùNpÛm NmT[m ìTôn 76

JÚ NR®¡Rj§tÏ 76

1

ìTôn 984.50, it is 76

1 x 984.50.

@100 dÏ 1295.39X10076

984.50=

100%ARôYÕ, ùUôjR NmT[m = ìTôn 1295.40.

ERôWQm 1 (Example 1)

200 ≠hPo ùLôs[[Ü ùLôiP úTW≠pCÚkÕ 75 ≠hPôó GiùQn ùY°úVGÓdLlTÓ¡\Õ G²p ùY°úV GÓjRGiùQn«u NR®¡RjûR LiÓ©¥.


43

¾ôóÜ

GÓdLlThP GiùQn«u NR®¡Rm =ùY°«p GÓdLlThP GiùQn (≠hPôõp)/ úTWp ùLôs[[Ü (≠hPôóv) x 100


15000/- ìTôndÏ E§¬ TôLm 15% XôTj§tÏYô¥dûLVô[ÚdÏ ®tLlTÓ¡\Õ G²p.¸rLiPYtû\ LiÓ©¥ (a) Yôe¡V ®ûXGu] (b) GqY[Ü XôTm. .

¾ôóÜ: ùTôÚ°u ®ûX (CP) = x ,

ùTôÚ°u ®ûX (CP) = cost price

®t\ ®ûX (SP) = sale price

®t\ ®ûX=ùTôÚ°u ®ûX+®t\®ûX«p15%

15000= +

XôTm = ®t\ ®ûX-ùTôÚ°u ®ûX = 15000-13043=1956.53

Yôe¡V ®ûX= Rs.13,043/,XôTm = Rs. 1957/


ùUôjRm 80000 Lôô óLû[ Å§«púNô§jRùTôÝÕ, A§p 16000 LôôóLs Gq®RÏû\LÞm CpXôUp CÚkRÕ G²pHtßdùLôs[lThP LôôóL°u NR®¡RmGqY[Üþ

=


úUôhPôôó ûNdLõs ®ûX 92% A[®tÏÏû\kÕ®hPÕ. AÕ RtùTôÝÕ ì 18000/-dÏ ®tTû] ùNnVlTÓ¡\Õ G²p ARuEiûUVô] ®ûX Gu].?

¾ôóÜ

RtùTôÝÕ úUôhPôôó ûNdL¡s ®ûXì. 18000/-

EiûUVô] ®ûX«p CRu U§l× 92% BÏm.

EiûUVô] ®ûX= 18000 x

= Rs.19565/-

ERôWQm 5 (E(E(E(E(Example 5)xample 5)xample 5)xample 5)xample 5)

JÚ úUôhPôôó YôL]m, JÚ U¦ úSWj§p 30¡úXô ÁhPôó úYLj§p ùNu\ôp 100 ≠hPôóùThúWôp ùNXYô¡\Õ. YôL]jûR TÝÕTôôójR ©u JÚ Sôû[dÏ 90 ≠hPWôLÏû\kÕ®hPÕ. G²p úNªlûTNR®¡Rj§p LQd¡Ó.

¾ôóÜ

úNªl× NR®¡Rj§p= Ïû\kR ÖLôóÜ/BWmTÖLôóÜ x 100

= (100 – 90) x100

=

= 10% GôõùTôÚs ªfNm


1 NÕWj§u TdLm =400mm (side of square)

®hPm = 400 ª.Á

L¯Ü = ______ %.

2 ®hPm (d) = 26ª.Á

ùYhÓ BZm ('a')depth of u/cut = 2.4ª.Á Ï ß d Ïù Y h Óú R ô t \ j § pT W l T [ Ü= ______ %



44

3 A§LôõdLlThPNR®¡Rm = 36%

A§LôõdLlThPU§l×

= 611.2 ¨ëhPuªÁ2

E i û U V ô ]CÝ®ûN=_____ ¨ëhPu/ª.Á2.

4 AXô«p Es[ùNm×= 27 ¡úXô

AXô«p Es[ÕjRSôLm = 18¡úXô

ùNm©u NRÅRm= ________%% ÕjR SôLj§uNR®§m = ______%.

5 AXô«u GûP= 140 KgfSn GûP = 40%Pb = ______ KgfSn = ______ Kgf.

6 ú`PhTÏ§ = ______ %.

7 A Ý j R l T h P¿[m = ______ %.

8 ®hPm (d) = 360 mm

TdLm (a) = 0.707 x d

L¯Ü = ______ %.

9 Cu = 36 ¡¡

Zn = 24 ¡¡

Cu = ______ %

Zn = ______ %

10 Cu = 42.3 ¡¡

Sn = 2.7 ¡¡

Cu ______ %

Sn = ______ %.

11 JÚ E§¬ TôLm ì.195/- dÏ YôeLlTÓ¡\Õ.CÕ ®tTû] YõûX«p 65% G²p ®tTû]®ûX GqY[Ü.

12 JÚ úUôhPôôó ûNd¡s PVôó ìTôn 300þdÏ ®tLlTÓ¡\Õ. C§p 25% XôTmúNodLlTh¥ÚkRôp. CRu Yôe¡V ®ûXGqY[Ü.

13 Lôt±p 23% Bd³_u Utßm 77%ûShW_àm CÚkRôp 120 L] ÁhPôóLôt±p GjRû] L]ÁhPôó êXLeLsEs[]?

14 JÚ ¼Np Gu£u úTôõe A[®p Es[êXlùTôÚhLs ¸úZ ùLôÓdLlThÓs[].

a) ùNm× (Cu) - 86%

b) ùYsÇVm (Sn) - 10%

c) ÕjR SôLm (Zn) - 4%

AXô«u GûP 40 ¡úXô BÏm. C§pJqùYôÚ êXLeL°u GûPûV LôiL.

15 BhúPô ôõlúTôó ùNnÙm úLúW_õpúNôpPôó TVuTÓjRlTÓ¡\Õ. A§p 35%ùYsÇVm Utßm 65% DVØm LXkÕEs[Õ. úNôXóPôõu GûP 40 ¡úXô Gu\ôpêXLeL°u GûPûV R²jR²úVLiÓ©¥dLÜm.

16 Lôôõp 4 ®RUô] TVQm ùNnVlTÓ¡\Õ.JqùYôÚ TVQj§u çWm 200 ûUpLsCkR SôuÏ TVQeL°Ûm ùThúWôpETúVôLm Øû\úV 6.65, 7.5, 6.85, Utßm7.05 úLXuLs BÏm.

¸úZ Es[ûYLû[ LiÓ©¥:

1 JqùYôÚ TVQj§u úTôÕm NWôNôõùThúWôp TVuTôÓ



45

2 JqùYôÚ ûUÛdÏm ùNXYô] NWôNôõùThúWôp

3 TVuTÓjRlThP NWôNôõ ùThúWôpNRÅRj§u A¥lTûP«p A§LUôLTVuTÓjRlThP ùThúWôûXNR®¡Rj§p á\Üm. CûR NôõVôLCWiÓ RNUj§tÏ LiÓ©¥dLÜm.

17 úTôdÏYWjÕ T¦Uû]«p, ØRÄhÓYÚUô]j§p ¸rLiP ùNXÜLsLiÓ©¥dLlThPÕ.

1 PVÚdLôL 40% YÚUô]mùNXY¯dLlThPÕ

2 GôõùTôÚs Utßm EVÜl ùTôÚÞdLôL30% YÚUô]m ùNXY¯dLlThPÕ

3 E§¬ TôLeLÞdLô] ùNXÜ 10%.

UôR Ø¥®p ì 2000/- úNªdLlTÓ¡\ÕGu\ôp ùUôjR YÚUô]m GqY[Ü.

18 JÚ Lôv¥e¡u GûP 80 ¡úXô¡Wôm.BWmTLhP ùU£²e¡p ARu GûP 4%Ïû\¡\Õ Ut\m Cß§LhP ùU£²e¡p5% GûP Ïû\¡\Õ G²p, ùU£²eùNnVlThP TôLj§u Cß§ GûPGu]YôL CÚdÏm.

19 25 ¡úXô¡Wôm GûPÙs[ Lôv¥e¡pÕjRSôLm 35% ùNm× 40% Utßm 25%ùYsÇVm CÚkRôp, R²jR²úVAYt±u GûP Gu]YôL CÚdÏm.

20 JÚ NôpP¬p 35% ùYsÇVm 65%. LôÃVmEs[Õ, C§p ùYsÇVj§u GûP 14¡Wôm G²p, NôpP¬u ùUôjR GûPGqY[Ü.

21 JÚ úNpvúUu UôR NmT[m ì 1000/--Utßm 2.5% úNpv Lª`]ôL ùTß¡\ôo.AYo JÚ YÚPj§p ì. 60,000/= -U§l©tÏúNpv ùNnÕ ùLôÓjRôp AY¬u ùUôjRYÚUô]m Gu]YôL CÚdÏm.

22 JÚ U²Ru Ru YÚUô]j§p 15%®YNôVj§tÏm, 21% ÏÓmTj§tÏm, 24%ÏZkûRLs Lp®dÏm Utßm úNªlTôLì 360/= ûL«p ûYj§ÚkRôp AY¬u UôRùUôjR YÚUô]m GqY[Ü?

23 JÚ U²Ru Rôu YôeÏm UôR YÚUô]mì 450/= p ì 90/= I úNªjÕ ûYjRôp,AY¬u úNªl× GjRû] NRÅRm CÚdÏm.



46

NRÅRj§≠ÚkÕ RNU©u]m Utßm NôRôWQ ©u]UôL UôtßRpT«t£ 1.5.16

NôRôWQ ©u]jûR NRÅRUôL UôtßRp.

1 NRÅRUôL UôtßL

¾oÜ: x 100

= 50%

2 111----- - -I NRÅRUôL UôtßL

¾oÜ: 111

x 100 = 11100

= 9.01%

¸rYÚm NôRôWQ ©u]eLû[ NRÅRUôLUôtßL.

1 41

2 51

3 32

4 83

NRÅRjûR NôRôWQ ©u]UôL UôtßRp.

1 24% -I NôRôWQ ©u]UôL UôtßL

¾oÜ: 10024

= 256

2 3133 % -I NôRôWQ ©u]UôL UôtßL

¾oÜ: 100

3133

= 100

13

100 100

3100

×=

= 31

¸rYÚm NRÅRjûR NôRôWQ ©u]UôLUôtßL.

1 15%

2 %2187

3 80%

4 125%

RNU©u]jûR NRÅRUôL UôtßRp.

1 0.35 - I NRÅRUôL UôtßL

¾oÜ: 0.35 x 100

= 35%

2 0.375 - I NRÅRUôL UôtßL

¾oÜ: 0.375 x 100

= 37.5%

¸rYÚm RNU©u]eLû[ NRÅRUôLUôtßL.

1 0.2

2 0.004

3 0.875

4 0.052

NRÅRjûR RNU©u]UôL UôtßRp.

1 30% - I RNU©u]UôL UôtßL

¾oÜ: 10030

= 0.3

2 %3133 - I RNU©u]UôL UôtßL

¾oÜ: 100

3133

= 100

13

100 100

3100

×=

= 31

= 0.333

¸rYÚm NRÅRjûR RNU©u]UôLUôtßL.

1 15%

2 7%

3 %2112

4 90%


47

CVtL¦Rd Ï±ÂÓLs Utßm A¥lTûPLs T«t£ 1.6.17

A±ØLm (Introduction)

ùR¬VôR GiL°u U§lûT ùR¬kÕ ùLôs[úYi¥V CPj§p, CVtL¦Rj§p,GÝjÕdLs TVuTÓjRlTÓ¡\Õ. CÕ JÚYûL L¦RUôÏm. CqYûL LQd¡p,GÝjÕdLÞPu GiLÞm úRûYlTÓmCPeL°p U§l©tÏ HtT TVuTÓjRlTÓ¡u\]. ERôWQj§tÏ 3X Utßm X3,CWi¥Ûm X þu CPm ®j§VôNlTÓ¡\Õ.3X þp 3 Gu\ Gi X þBp ùTÚdLlThÓs[Õ.B]ôp X3 þp 3 Gu\ Gi Xþu Index BLEs[Õ.

Tô£¥q Utßm ùSL¥q GiLs (Positiveand negative numbers)

Tô£¥q GiLÞdÏ Øu]ôp + Ï±ÂÓmUtßm ùSL¥q GiLÞdÏ Øu]ôp þÏ±ÂÓm Ï±dLlTÓm. CúR Øû\ûVGÝjÕdLÞdÏm SûPØû\TÓjRlTÓ¡\Õ.

ERôWQm (Example)

+ X, - Y

+8 (A) 8 Guß Tô£¥q GiûQd Ï±dLXôm.

þ8 GuTÕ ùSL¥q GiQôÏm.

áhPp Utßm L¯jRp (Addition and subtrac-tion)

CWiÓ Tô£¥q GiLû[ áhÓm úTôÕ,ARu A[ÜLs áh¥, ARu Øu×\j§páhPp Ï±ûV Ï±dL úYiÓm.

CWiÓ ùSL¥q GiLû[ áhÓm úTôÕ,ARu A[ÜLs áh¥, Øu×\j§p L¯jRpÏ±ûV Ï±dL úYiÓm.

Tô£¥q Utßm ùSL¥q GiLû[ áhÓmúTôÕ ARu A[ÜL°u ®j§VôNjûRÏ±dL úYiÓm. úUÛm C§p GkR A[ÜùT¬VRôL Es[úRô ARu Ï±ÂhûP ØuTdLm Ï±dL úYiÓm.

+ 7+ 22 = + 29

- 8 -34 = -42

- 27 + 19 = - 8

44 + (-18) = +26

37 + (-52) = (-15)

Tô£¥q Utßm ùSL¥q GiLû[ùTÚdÏRp (Mulitiplication of positive andnegative numbers)

JúW Ï±ÂÓ Es[ CWiÓ Tô£¥q GiLû[ùTÚd¡]ôp ARu ùTÚdÏj ùRôûLûV +Ï±ÂhPôp Ï±dL úYiÓm. LY²dL,CWiÓ ùTÚdÏ GiLÞm ùSL¥q BLCÚkRôp ARu ùTÚdÏ ùRôûL + Tô£¥qBÏm.

ERôWQm (Example)

– 20 x –3 = 60

5 x 8 = 40

4 x –13 = –52

–5 x 12 = –60

YÏjRp (Division)

YÏTÓm Gi YÏdLlTÓm GiQôpYÏdLlTÓ¡\Õ. CqYôß YÏjRôp YÚm®ûP DÜ G]lTÓ¡\Õ. YÏTÓm GiÔmYÏdLlTÓm GiÔm JúW Ï±ÂhPôLCÚkRôp, DÜ + áhPp Ï±VôÏm. ùYqúYßÏ±ÂÓLs CÚkRôp ARu ®ûPûV þ ùSL¥qÏ±ÂPôL Ï±dL úYiÓm.

JÚ LQd¡p áhPp, L¯jRp,ùTÚdLp, Utßm YÏjRp CÚkRôpØR≠p ùTÚdLp Utßm YÏjRÛmARu ©\Ï áhPp Utßm L¯jRÛmùNnV úYiÓm.

ERôWQm (Example)


48

AûPl×dÏ±Ls Utßm Ï±Âh¥uùRôÏ§ (Parenthesis and grouping symbols)

( ) ©WôdLh (Brackets)

{ } ©úWNv (Braces)

7 + (6 - 2) = =4 = 11

6 X (8 - 5) = 6 X 3 =18

AûPl×dÏ±Ls (Parenthesis)

CkR YûL Ï±ÂÓLs £X áhPp UtßmL¯jRûX, ùTÚdLp Utßm YÏjRÛdÏØu]ôp ùNnV úYiÓm. Á§ úYûXLû[ùNnYRtÏ Øu CRtÏs Es[ Ï±l©hPúYûXLû[ ØÝûUVôL Ø¥dL úYiÓm.Ï±Âh¥u ùRôÏ§ Ø¥kR ©\Ï, Ï±ÂÓLû[¿dLÜm.

Ï±Âh¥u ùRôÏ§ûV EP]¥VôL ØuTdLmÏ±dL úYiÓm. (A) GiLÞdÏ Øu]ôpÏ±dL úYiÓm. B]ôp Ï±ÂÓCpûXùV²p Sôm ùNnV úYi¥V ®`VmùTÚdLp GuTûRd ×¬kÕ ùLôs[ úYiÓm.

L¯jRp Utßm ùSL¥q GiLû[ ùTÚdLpùNnÙm ùTôÝÕ Ï±Âh¥u ùRôÏ§ûVTVuTÓjR úYiÓm.

ùSL¥q Ï±ÂÓ Øu]ôp Es[ Ï±Âh¥uùRôÏ§ûV ¿dÏm úTôÕ, Ï±Âh¥uùRôÏ§«p Es[ GpXô Ï±ÂÓLû[ÙmUôt\ úYiÓm. (+ Ï±Âh¥p CÚkÕ þÏ±ÂhÓdÏm Utßm þ Ï±Âh¥p CÚkÕ +Ï±ÂhÓdÏm Uôt\ úYiÓm.)

AûPl×d Ï±Ls Øu + Ï±ÂÓ CÚkRôpÏ±ÂÓL°u úLôûYLû[ Uôt\ôUp +Ï±ÂÓLû[ ¿dLXôm.

Ï±Âh¥u JÚ ùRôÏ§ Utù\ôÚùRôÏ§ÙPu ùTôÚk§ CÚkRôp, ØRpùNh¥u ªLÜm AÚ¡p Es[ûR ¿dLúYiÓm.

ùTôÕYô] A[ÜLs + ApXÕ þ Ï±Âh¥uêXm CûQdLlTh¥ÚkRôp CkRùTôÕYô] A[Ü AûPl×d Ï±dÏ ØuTôLûYdL úYiÓm.

8 + 6 (4-1) = 8 + 6 X 3 =36

(6+2) (9 -5) = 8 X 4 =32

áhPp + 4, ùSL¥q þ 7 CûR 4 þ (þ 7) GußGÝR úYiÓm.

áhPp + 4, - - I 7 Bp ùTÚdL 4(-7) Guß GÝRúYiÓm.

4 - (-7) = 4+7 =11

8 - (7 -4) = 8 - 3 = 5

3 + (- 8) = 3 - 8 = -5

7 + (4 - 19) = 7 + (-15) = 7 - 15 = - 8

3 {40+ (7 +5) (8 - 2)} =3 {40+12 X 6} = 3 X 112 = 336

8x + 12 C§p 4 þI LôW¦VôL TVuTÓj§]ôp

8x + 12 GuTÕ 4 (2x +3) G]lTÓm.

EhTÏ§«Ûs[ Ï±Âh¥u ùRôÏ§ûVØR≠p ÑÚdL úYiÓm.

CVtL¦R Ï±ÂÓLs Utßm JÚ T¥fNUuTôÓLs (Algebric symbols and simple equa-tions)

CVtL¦R Ï±ÂÓLs (Algebric symbols)

ùR¬VôR GiL°u U§l× GÝjÕdLs êXmÏ±dLlTÓ¡\Õ. CÕ CVtL¦R Ï±ÂPôÏm.

LôW¦ (Factor)

LôW¦ GuTÕ GiLs (A) GÝjÕdLs (A)ùRôÏ§ BÏm. HRôYÕ Ju\ôL CÚdLXôm.AûY ùTÚdÏm úTôÕ ¡ûPdL á¥VûY

Gdv©Wù (expression) BÏm. 12þu LôW¦Ls

4 Utßm 3 (A) 6 Utßm 2 (A) 12 Utßm 1.

8x+12 Gu\ Gdvl©W`û] CqYôßLôW¦TÓj§ GÝRXôm.

4 (2x + 3), 4 Utßm (2x + 3) LôW¦Ls BÏm.

CVtL¦R úLôûYLs (Algebris terms)

JÚ Gdv©W`²p CWiÓ ApXÕCWiÓdÏ úUtThP TÏ§Ls R²jR²VôLCÚkRôp ARôYÕ + (A) þ, JqùYôÚ TÏ§ÙmúLôûYLs G]lTÓm.

Y - 5x GuTÕ GdvlW`]ôÏm, Y Utßm - 5xGuTÕ úLôûYLs BÏm.

úLôûYLÞdÏ Øu]ôp Ï±ÂÓ Ï±dLúYiÓm.

ÏQLm (Co-efficient)

JÚ GdvlWù LôW¦L[ôL AûUdLlùTt\ôp ARu ùTÚdÏj ùRôûLGdvlWù BÏm. ©\Ï JqùYôÚ LôW¦ÙmÁRØs[ LôW¦L°u ÏQLm BÏm.

12x þu ÏQLm 4 BÏm.

48 þu ÏQLm x BÏm.



49

NUuTôÓ (Equation)

CWiÓ GiLÞdÏ CûPúVVô] NU¨ûX(A) GiLs Ut\m CVtL¦j Ï±ÂÓLsNUUôL CÚl©u CÕ NUuTôÓ G]lTÓm.

JÚ T¥f NUuTôÓ (Simple Equation)

ØRp AÓd¡u (Power) CVtL¦R Ï±ÂÓPuCÚkRôp AÕ JÚ T¥fNUuTôÓ G]lTÓm.

áhPp Utßm L¯jRp (Addition and subtrac-tion)

JúW Ï±ÂÓ Utßm AÓdÏLs (power)ùLôiP úLôûYLs BL CVtL¦RÏ±ÂhÓPu Gi¦dûL CÚkRôp áhPpUtßm L¯jRp ùNnVXôm.

10x + 14 – 7y2 – 11a + 2x – 4 – 3y2 – 4a + 8

= 10x + 2x – 7y2 – 3y2 – 11a – 4a + 14 – 4 + 8

= 12x – 10y2 – 15a + 18

2x = 10, 2x + 6 = 10 + 6

y + 12 = 20, y + 12 – 8 = 20 – 8

x + 10 = 12,

x + 10 – 10 = 12 – 10

3x = 6, 2 x 3x = 2 x 6, 6 x = 12

5y = 20, 5

20 =

5

5y

NUuTôhûP UôßRp ùNnVôUp JúWYûLVô] GiLû[ áhPXôm UtßmL¯dLXôm.

NUuTôh¥u JqùYôÚ Eßl×Lû[Ùm AúRGiL[ôp ùTÚdLúYô (A) YÏdLúYôùNnVXôm. (NUuTôh¥u NU¨ûXjRuûUûV Uôt\ôUp).

GiLs ApXÕ Ï±ÂÓLû[ CWiÓ TdLØmáhÓRp (A) L¯jRp ùNnÙm úTôÕNUuTôh¥u NU¨ûX Uô\ôÕ. AúRúTôpùTÚdLp Utßm YÏjRp ùNnÙm úTôÕAúR GiLs (A) Ï±ÂÓLs CWiÓ TdLØmùNnÙm ùTôÝÕ NU¨ûXj RuûUûVTô§dLôÕ.

JÚ T¥ NUuTôh¥p úLôûYL°u Y¬ûNUôßTÓm úTôÕ (Transposition of the terms ofthe equations)

= NUm

+ áhPp

þ L¯jRp

X ùTÚdLp

YÏjRp

NUuTôh¥u RjÕYm (Concept of equality)(TPm 1)

NUuTôhûP JÚ _ûR vúLÛPu Jl©ÓmúTôÕ, CûY GlúTôÕm NUUôL CÚdÏm.CÚ TdLØm Es[ NUuTôhûP Uôt±AûUjRôÛm NUUôLúY CÚdÏm. 9 = 5 + xGuTûR 5+x = 9 Gußm GÝRXôm.

CÚ TdLØm Es[ NUu TôhûP CúRØû\«p ùNnÕ NUuTÓjR úYiÓm. JúWU§lûT CWiÓ TdLØm áhPúYô (A)L¯dLúYô ùNnVXôm. 5+ x = 9 EPu CÚTdLØm 3þI áhPÜm. CqYôß ùNnRôp, 5+x+ 3 = 9 + 3 (A) X+8 =12 BL NUuTôÓ B¡®Óm.5 + x = 9 C§≠ÚkÕ 5þI CWiÓ TdLØmL¯dLÜm. ©\Ï 5+ x - 5 = 9 -5. x =4.

5þI CPÕ Utßm YXÕ TdLm Uôt±AûUjRôp Ï±ÂÓLû[ + p CÚkÕ þ dÏUôt\Üm.



50

4

x = 20 CWiÓ TdLØm 4 þ Bp ùTÚdLÜm.

©\Ï 4

x x 4 = 20 x 4.

X = 80

5x = 25

CWiÓ TdLØm 5 þBp YÏdLÜm

©\Ï 5

25 =

5

5x = x = 5

GiLs ApXÕ Ï±ÂÓ GÝjÕLs JÚTdLj§≠ÚkÕ AÓjR TdLm Uô±]ôp,ùTÚdLp YÏjRXôÏm, YÏjRpùTÚdLXôLÜm Uôßm.

CWiÓ TdLØm Es[ NUuTôhûPNUUôL LÚ§ ùNVpTÓm ùTôÝÕNUuTôh¥u NU¨ûXUôßTÓY§pûX.

JÚ TdLj§≠ÚkÕ Utù\ôÚTdLj§tÏ Uôt\lThPôp áhPpA[Ü L¯jRp A[YôL Uôß¡u\Õ.

L¯jRp A[Ü áhPp A[YôLUôß¡u\Õ.

ùTÚdLp YÏjRXôL Uôß¡u\Õ.

YÏjRp ùTÚdLXôL Uôß¡u\Õ.

JÚ T¥f NUuTôh¥u ¾oÜLôQAf NUuTôh¥u CPÕ TdLmùR¬VôR GiL°u U§lûTR²ûUlTÓjÕYRu êXm G°VNUu Tôh¥tÏ ¾oÜ Ø¥Ùm.

ERôWQm (Example)

¾oÜ LôiL.

4x = 3(35 – x ) Gu\ôp x þu U§lûT LôiL.

4x = 105 – 3x (AûPl× Ï± ¿dLlThÓ®hPÕ)

4x + 3x = 105 (-3x þI YXÕ ×\j§p CÚkÕCPÕ ×\j§tÏ UôtßL)

7x = 105

x = 15 (CWiÓ TdLØm 7 Bp YÏdLÜm).



51

CVtL¦Rj§p Es[ ©¬Yô] áhPp, L¯jRp, ùTÚdLp UtßmYÏjRp T«t£ 1.6.18

áhPp

ERôWQm 1

áhÓL 2x, 3x, 7x

¾oÜ : C§p ùYßm áhPp UhÓmCÚlTR]ôp JqùYôÚ AûPl×dÏsÞm ‘+’Ï±ÂÓ ùNnVÜm.

= (+2x) + (+3x) + (+7x) = 12x

áhÓL

-3a, -2a, -5a

= (-3a) + (-2a) + (-5a) = -10a

ERôWQm 2

áhÓL 10xy, -8x2, -7xy, -7x2

= (10xy) + (-8x2) + (-7xy) + (-7x2)

= (10xy) + (-7xy) + (-8x2) + (-7x2)

= (3xy) + (-15x2)

ERôWQm 3

áhÓL 8a

,2a

,4a

−

L¯jRp

ERôWQm 1

2 ÁhP≠ÚkÕ 8 ÁhPûW L¯dLÜm

¾oÜ : (2m) - (8m)

+8 -≠ÚkÕ L¯dL úYiÓm Uôt±V©u + 2m Ï±ÂÓ - 8m

áh¥V©u - 6m

ERôWQm 2

L¯jRp (-5x + 3y) from (7x + 8y)

¾oÜ: (7x + 8y) - (-5x + 3y)

+ 7x + 8y

+ 5x - 3y

+ 12x + 5y

‘-’ Ï±ÂhÓPu Es[ Aû]jÕ úLôûYLû[Ùm (terms) ùTÚdLÜm. ARàPu áhPpUtßm L¯jRp ùNnV úYi¥V úLôûYLû[¸úZ ùNôp≠V vùPl£uT¥ ùNnVÜm.

G°V NUuTôÓLÞdÏ ¾oÜ LôÔRp

CVtL¦R Ï±Âh¥tLô] E\Ü ®§Ls

1 ùTÚdLp ®§Ls

(i) + x + = +

(ii) - x - = +

(iii) + x - = -

(iv) - x + = -

2 YÏjRp ®§Ls

(i)

(ii) +=−−

(iii) −=−

+

(iv) −=+−

ERôWQeLs

1) a + 4 = 7

a = 7 - 4

a = 3

2) M - 5 = 3

m = 3 + 5

m = 8

3) 7P = 17

P = 7

17

4)6x

= 9

x = 9 x 6

x = 54

5) 7x + 3 = 15 + x

7x -x = 15 - 3

6x = 12


52

x = 6

12= 2

6) 0y9

5=

Y = 0 x 5

9

y = 0

45

810M

852XM

2M58

68M58

86M58

==

=

=

−=

=+7)

36x

365

6 x 30x

6 x 305x

306

3x 2x

302

x

3

x

=

==

=

=+

=+8)

1443

12 x36x

36123x

3612

2x -5x -4x 6x

36 6x

125x

3

x

2

x

36 6x

125x

3

x

2

x

==

=

=+

=−−+

+=−+9)

30- a

8 x 0 30 a

0830 a

08

30 4a - 5a

0 4

152

aa

8

5

=

=+

=+

=+

=+−10)

ùTÚdLp

ùTÚdLp ùNnÙm ùTôÝÕ ØR≠p GpXôÏ±ÂÓLû[Ùm, ©u× ÏQLeLû[Ùm ARu©\Ï GÝjÕLû[Ùm ùTÚdLÜm.

ERôWQm 1

ùTÚdÏL (2x-5) x (x-1)

(2x-5) (x-1)

= 2x (x-1) - 5(x-1)

= 2x2 - 2x -5x +5

= 2x2 - 7x + 5

ERôWQm 2

ùTÚdÏL (4x2 + 3x -12) by (2x +3)

(4x2 + 3x -12) (2x +3)

= 2x(4x2 + 3x -12) + 3 (4x2 + 3x -12)

= 8x3 +6x2 - 24x + 12x2 + 9x - 36

= 8x3 +6x2 + 12x2 - 24x + 9x - 36

= 8x3 +18x2 - 15x -36

YÏjRp

YÏjRp GuTÕ ùTÚdL≠u G§o Uû\ùNnûLVôÏm.

ERôWQm 1

YÏjRp (x2+ 11x + 30) by (x + 6)

(x2+ 11x + 30) ÷ (x + 6)

x2+ 11x + 30 ÷ x + 6 = x + 5



53


áhPp

1 Add 7y, 8y, 5y , 3y

2 Add 5x, 6x, 7y - 9y, 10x

3 Add 9a2, -7m, 5, -14a2, 15m, -6

4 Add

L¯jRp

1 Subtract 7x from 9x

2 Subtract 8a from 3a

3 (-5 -3b) - (3a + 5b)

4 Subtract (5m - 6n) from (3m + 5n)

ùTÚdLp

1 Multiply 6a x (- 2ab)

2 Multiply 3x (4x - 2y + 5)

3 Multiply (3x + 2) (3x - 2)

YÏjRp

1 525x ÷

2 15a60ab ÷

3 77y14x ÷−



54

EúXôLeL°u CVt©Vp Utßm CVk§W®Vp RuûULs T«t£ 1.7.19

EúXôLm: (Metal)

EúXôLm GuTÕ JÚ RôÕlùTôÚs.CûYGpXô ®RUô] ùTô±«Vp úYûXLÞdÏmTVuTÓjRlTÓ¡\Õ. ARôYÕ CVk§WeLs,TôXeLs, BLôV®Uô]m úTôu\Yt±pTVuTÓjRlTÓ¡\Õ. BûLVôp SômEúXôLj§u A¥lTûP A±ûY ùTt±ÚdLúYiÓm.

ùYlTm EVoRp, CÝ®ûN, CßdÏ®ûNUtßm úUôRXôp HtTÓm ®ûN úTôu\LôW¦LÞdÏ HtT Y¥YûUdLlThP TXYûLVô] TôLeLû[ JÚ ùU£²vhùNnYRtÏ Øu EúXôLeL°u CVt©VpUtßm CVk§Wj RuûUL°uØd¡VjÕYjûR ×¬kÕ ùLôiPYWôLCÚjRp ªL Ød¡V úRûYVôÏm.

EúXôLj§u RuûULû[ A±kÕ CÚjRpúYûXûV ùYt±LWUôL ùNnÕ Ø¥dL ERÜm.N¬Vô] êXlùTôÚs/EúXôLm TVuTÓj§TôLeLs ùNnVlTPô®hPôp, AlTôLeLsETúVôLj§p CÚdÏm ùTôÝÕEûPYRtúLô ApXÕ úRôp®«pØ¥YûPYRtúLô Yônl× HtTÓm.

EúXôLj§u ÁÕ JúW A[®p TÞùLôÓdÏmúTôÕ TpúYß EúXôLeL°pHtTÓm ®û[ÜLû[ (TPm 1) LôhÓ¡\Õ.EÚUôt\j§u ®û[ÜLÞdLô]®j§VôNj§û] Ï±jÕd ùLôs[Üm.

– LhPûUl×

– LPjÕm RuûU

– LôkRj RuûU

– EÚÏm RuûU

¨\m (Colour)

JqùYôÚ EúXôLj§tÏm CVtûL«úXúVR²jR² ¨\m EiÓ. ERôWQm ,ùNm×®j§VôNUô] £Ll× ̈ \j§p CÚdÏm, ªÚÕG@Ï FRô/LÚl× ¨\j§p CÚdÏm.

GûP (Weight)

JÚ Ï±l©hP L] A[Üs[ EúXôLeL°uGûP JtßdÏ Juß UôßTÓm.AÛª²Vj§u GûP Ïû\YôL CÚdÏm(APôój§ Gi 2.7) Utßm LôÃVj§u GûPA§LUôL CÚdÏm (APôój§ Gi 11.34)

LhPûUl× (Structure) (TPm 2 & 3)

JÚ EúXôLj§u ÏßdÏ ùYhÓ úRôt\jûRûUdúWôvúLôl êXm EúXôLeL°uAûUl©u ®j§VôNjûR A±VXôm.ùTôÕYôL EúXôLeL°u Eh×\ AûUl×ùYqúY\ôL CÚdÏm. úR²Úm× UtßmAÛª²Vj§u AûUl× Sôôó úTôußCÚdÏm Utßm Yôôól©Úm× UtßmùYiLXm ¡WôàXôó AûUl× ùLôiPRôLCÚdÏm.

EúXôLj§u CVt©Vp RuûULs (Physi-cal properties of metals)

– ¨\m

– GûP/APôój§ Gi


55

LPjÕm RuûU (Conductivity) (TPm 4 & 5)

ùYlTdLPjRp Utßm ªuLPjRp RuûUJÚ RÏ§Vô] ùTôÚ°u ùYlTjûRÙm,ªuNôWjûRÙm LPjÕm §\]ôÏm.LPjÕmRuûU JußdùLôuß UôßTÓm.ùNm×m AÛª²VØm JÚ SpX ùYlTmUtßm ªu LPj§VôÏm.

LôkRj RuûU (Magnetic property)

JÚ EúXôLm LôkRj§]ôp LYWlThPôpAkR EúXôLm LôkRjRuûU EûPVÕ GußùNôp¡ú\ôm.

£X YûL vùP«uùXv v¼pLû[j R®W,ùTÚmTôÛm GpXô CÚm× NjÕ Es[EúXôLeLÞm LôkRjRôp LYWlTÓm UtßmGpXô ®RUô] CÚm× NjÕ CpXôREúXôLeLs Utßm ARàûPV AXônB¡VYûY LôkRm LYWôÕ.

EÚÏm RuûU (Fusibility) (TPm 6)

EúXôLj§u ÁÕ ùYlTjûR ùNÛj§]ôp,§iU ¨ûX«p CÚkÕ ¿ôóU ¨ûXûVAûPÙm RuûU EÚÏm RuûU G]lTÓm.TX EúXôLeL°u EÚYj§p UôßRpHtTÓm. ARôYÕ ùYqúYß ùYlT¨ûX«pEúXôLeLs §iU ¨ûX«p CÚkÕ ¿ôóU¨ûXûV AûP¡u\Õ. Ïû\kR ùYlT¨ûX«p LôÃVm EÚÏm. AúR NUVm CÚm×A§L ùYlT ¨ûX«pRôu EÚÏm.

ùYsÇVj§u EÚÏ ¨ûX 232°C.

PevPu EúXôLj§u EÚÏ ¨ûX 3370°C.

CVk§W®Vp RuûULs (Mechanicalproperties)

– Lm©VôL ¿Þm RuûU (Ductility)

– RLPôL ¿Þm RuûU (Malleability)

– L¥]j RuûU (Hardness)

– ùSôßeÏm RuûU (Brittleness)

– §iûUj RuûU (Toughness)

– CÝ®ûNûV RôeÏm RuûU (Tenacity)

– Áh£j RuûU (Elasticity)

Lm©VôL ¿Þm RuûU (Ductility) (TPm 7)

Jo EúXôLjûR Lm©VôLj RVô¬dÏmùTôÝÕ, AÕ GkR ®R ®¬NÛdÏmEhTPôUp Lm©VôL ¿iPôp ARtÏLm©VôL ¿Þm RuûU Guß ùTVo. Lm©VôL¿Þm RuûUûVl ùTôßjÕ Ko EúXôLmLm©VôL Uôßm. CkRj RuûU EûPVEúXôLm Eß§Vô]RôLÜm Utßm ©[ôv¥d RuûUÙPàm CÚdL úYiÓm. ùNm×Utßm AÛª²Vm B¡VûY CjRuûUdÏ£\kR ERôWQUôÏm.



56

Áh£j RuûU (Elasticity)

EúXôLeLs ÁÕ JÚ Ï±l©hP A[Ü YûWYõûN ùNVtTÓmùTôÝÕ AlùTôÚ[ô]ÕEÚY UôßRp AûPkÕ, ©u Aq®ûN®ÓThPÜPu ÁiÓm Ru TûZV ̈ ûXûVAûPÙm RuûUdÏ Áh£j RuûU GußùTVo. ùYlT TR²Ó ùNnVlThP v©ôõeJÚ SpX ERôWQm BÏm.

RLPôL ¿Þm RuûU (Malleability) (TPm 8 &9)EúXôLeL°u ÁÕ Ñj§VXôp A¥jRpApXÕ úWô≠e ùNnÕ GpXô §ûNL°Ûm®ôõYûPkÕ AR]ôp ®¬N≠u± RLPôLUôßm RuûU RLPôL ¿Þm RuûU G]lTÓm.LôÃVm RLPôL ¿Þm RuûUdÏ £\kR EúXôLERôWQUôÏm.

L¥]j RuûU (Hardness) (TPm10)úRnUô]jûR RôeÏYûRÙm EWÑmúTôÕúRnYûPYûRÙm ¸\pLs HtTÓYûRÙmG§ôódÏm RuûU L¥]jRuûU G]lTÓm.AWjRôp Ï±ÂÓ ùNnÕ L¥]j RuûUûVúNô§jÕ A±VXôm.

ùSôßeÏm RuûU (Brittleness) (TPm 11)

EúXôLeLs EûPÙYRtÏ Øu]ôp ¨WkRWEÚY Uôt\j§tÏ B[ôLôUp EûPÙmRuûU BÏm. Yôôól©Úm× JÚ £\kRERôWQUôÏm. CÕ A§oÜ (A) úUôR≠]ôpYû[VôUp ùSôßeÏm RuûU EûPVRôÏm.

§iûUj RuûU (Toughness) (TPm 12)

EúXôLeLs úUôRXôúXô A§ôóf£VôúXôEûPVôUp AûR G§ôóójÕ ̈ tÏm RuûUúV§iûUj RuûU G]lTÓm. úR²Úm× CRtÏJÚ £\kR ERôWQUôÏm.

CÝ®ûNûV RôeÏm RuûU (Tenacity)

EúXôLeLs ÁÕ CÝ®ûNLsùNVpTÓmùTôÝÕ EûPVôUp G§ôójÕCÚdÏm RuûU CÝ®ûNûV RôeÏm RuûUG]lTÓm. ªÚÕ G@Ï, úR²Úm×, UtßmùNm× B¡V EúXôLeLs ùP]ô£h¥dÏ£\kR ERôWQeLs BÏm.



57

CÚm× Utßm Yôol× CÚm©tLô] A±ØLm T«t£ 1.7.20

CÚm×fNjÕs[ EúXôLeLs (Ferrous Met-als)A§L A[®p CÚm×NjÕ ùLôiPEúXôLjûR CÚm×fNjÕs[ EúXôLm G]AûZd¡ú\ôm. TpúYß úRûYLÞdÏTpúYß RuûUÙûPV CÚm×fNjÕs[EúXôLeLs TVuTÓjRlTÓ¡u\].

CÚm×, Yôol× CÚm×, úR²Úm×, UtßmG@Ï B¡VYt±u A±ØLm

ùTôÕYô] TVuTôh¥p Es[ CÚm×fNjÕs[ EúXôLeL[ôY]:

– L² CÚm× (Pig Iron)

– Yôol× CÚm× (Cast Iron)

– úR²Úm× (Wrought Iron)

– G@Ï Utßm LXl× G@Ï (Steels and Alloysteels)

CÚm× Utßm G@ÏLs TX ùNnØû\Lû[TVuTÓj§ RVôo ùNnVlTÓ¡\Õ.

L² CÚm× (Pig Iron) RVô¬dÏm Øû\

úY§Vp RuûU EûPV CÚm×fNjûRÏû\jÕ L² CÚm× ¡ûPdLl ùTß¡\Õ.CqYôß CÚm×fNjûR Ïû\jÕ L² CÚm×RVô¬dÏm Øû\ûV vùUp¥e (SMELTING)Guß A±¡ú\ôm.

L² CÚmûT RVô¬dLj úRûYVô]êXlùTôÚhLs;

– CÚm× RôÕ (Iron ore)

– Tô§ ÑhP ̈ XdL¬ (Coke)

– C[d¡ (Flux)

CÚm× RôÕ (Iron ore)

TVuTÓjRlTÓm Ød¡V CÚm× RôÕdLs.

– úUd]ûPh (magnetite)

– úaUûPh (hematite)

– ≠úUôû]h (limonite)

– LôoTú]h (carbonate)

úUtá±V RôÕdL°p CÚm× TX®¡ReL°pLXkÕ Es[Õ úUÛm CûYLs CVtûLVôL¡ûPd¡u\].

Tô§ ÑhP ¨XdL¬ (Coke)

Tô§ ÑhP ̈ XdL¬ úRûYVô] A[®tÏ CÕùYlTjûR ùLôÓdL G¬lùTôÚ[ôLTVuTÓjRlTÓ¡\Õ. úLôd¡p, LôoTuúUô]ôdûNPôL Es[ LôoTu RôÕÜPuúNokÕ CÚmTôL Uôt±d ùLôÓd¡\Õ.

C[d¡ (Flux)

CÕ JÚ RôÕl ùTôÚs FÕ EûX«u (Blastfurnace) A¥lTôLj§p ùNÛjRlTÓ¡\Õ. CRuêXm RôÕdLs EÚÏ ̈ ûXûV AûP¡u\Õ.CÕ EúXôLUt\ TÏ§ÙPu CûQkÕ EÚ¡VLNPôL EÚYô¡u\Õ.

FÕ EûX«p ùTÚmTôÛm ÑiQôm×LtLû[úV C[d¡VôL TVuTÓjÕ¡u\]o.

L² CÚm©u RuûULs Utßm TVuLs(Properties and use of Pig-iron)L² CÚmûT Ñj§L¬jÕ Utßm ÁiÓmEÚd¡ TX®RUô] CÚm× Utßm G@ÏLsRVôo ùNnVlThÓ TVuTÓjRlTÓ¡\Õ.

Yôol× CÚm× Cast Iron (RVô¬dÏm Øû\)

L² CÚm×, FÕ EûX«p CÚkÕ LNPôL,WôùUh¥¬VXôL ÏlúTôXô®p ùNÛjÕYRtLôL AÕ ÁiÓm Ñj§L¬dLlTÓ¡\Õ.CqYôß Ñj§L¬dLlThPÕ ÏlúTôXôEûX«u CPlTÓ¡\Õ CÕ JÚ £±V FÕEûXVôÏm.

ùTôÕYôL ÏlúTôXô EûX FÕ EûX úTôXùRôPokÕ úYûX ùNnVôÕ. úRûYlTÓmùTôÝÕ UhÓm AûR TVuTÓj§dùLôs[Xôm.

Yôol× CÚm× (YûLLs) (Cast Iron)CÚm×, LôoTu Utßm £≠dLôu LXûYRôuYôol× CÚmTôÏm. C§p 2 ØRp 4 ®ÝdLôÓLôoTu Es[Õ.

Yôol× CÚm©u YûLLs

Yôol× CÚm©u YûLLs ¸úZùLôÓdLlThÓs[];

– NômTp ¨\ Yôol× CÚm× (Grey cast iron)

– ùYsû[¨\ Yôol× CÚm× (White cast iron)

– úU≠V©p Yôol× CÚm×(Malleable cast iron)

– Öi EÚiûP Yôol× CÚm× (Nodular castiron)


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NômTp ¨\ Yôol× CÚm× (Grey cast iron)

CVk§Wj§u TôLeLû[ RVô¬dL Utßm ªLG°§p ùU£²e ùNnV NômTp ¨\ Yôol×CÚm× A§L A[®p TVuTÓjRlTÓ¡\Õ.

CVk§Wj§u A¥lTôLm, úP©sLs,TdLeLs B¡VûYLs Yôol× CÚmTôpùNnVlTÓ¡\Õ. Hù]²p Sôs TPEûZdÏm Utßm A[ÅPôL ¨ûXVôLCÚdÏm.

C§p ¡WôlûTh LXkÕ CÚlTRôp, úT¬eUtßm SLÚm TWl× Yôol× CÚmTôpùNnVlTÓ¡\Õ.

CÚmûTdLôh¥Ûm CRu EÚÏ ̈ ûX Ïû\Ü.£\kR §WYUôLÜm, £dLXô] Yôol×Lû[ùNnVÜm NômTp ¨\ Yôol× CÚm×TVuTÓ¡\Õ.

CVk§W LÚ®Lû[ ùNnYRtÏ NômTp ¨\Yôol× CÚm× A§L A[®pTVuTÓjRlTÓ¡\Õ Hù]u\ôp A§of£ûVÏû\d¡u\Õ, Utßm LÚ® ¡Ó ¡Ó G]BÓYûR RÓd¡u\Õ.

NômTp ̈ \ Yôol× CÚm× LXl× EúXôLUôLCpXôUp CÚkRôp CÝ®ûN ªLÜmÏû\YôL Es[Rôp G°§p EûPkÕ ®Óm.CdLôWQjRôp A§L ®ûN ApXÕ §¼ùW]HtTÓm TÞ YWdá¥V CVk§W TôLeLsCR]ôp RVôo ùNnVlTÓYÕ CpûX.

¨dLp, ÏúWôªVm, Y]¥Vm ApXÕ ùNm×B¡VûY TX úSWeL°p NômTp ̈ \ Yôol×CÚm×Pu LXkÕ L¥]jRuûUEiPôdLlTÓ¡\Õ.

NômTp ¨\ Yôol× CÚmûT Tt\ ûYdLCVÛm. B]ôp A¥lTûP EúXôLjûRØR≠p ùYlTlTÓjRúYiÓm.

ùYsû[ ̈ \ Yôol× CÚm× (White cast iron)

CÕ ªLÜm L¥]Uô] EúXôLm, ùU£uùNnYÕ L¥]m. AR]ôp úRnUô]jûRG§odÏm CVk§Wj§u TôLeLû[ RVôoùNnV TVuTÓjRlTÓ¡\Õ.

£≠dLôû] Ïû\jÕ Utßm úYLUôL Ï°o®jRp êXm ùYsû[ Yôol× CÚm×RVô¬dLlTÓ¡\Õ. CqYôß Ï°o®lTRôpCÕ Ï°okR Yôol× CÚm× GußmAûZdLlTÓ¡\Õ..

ùYsû[ Yôol× CÚmûT Tt\ ûYdLCVXôÕ.

úU≠V©p Yôol× CÚm× (Maileable castiron)

úU≠V©p Yôol× CÚmûT NômTp ¨\Yôol× CÚm×Pu Jl©Óm ùTôÝÕPd¥≠¥, CÝ®ûN, §iûUj RuûUB¡VûY áÓRXôL CÚd¡u\Õ.

ùYsû[ Yôol× CÚmûT ¿iP úSWm ùYlTTR²ÓRp ARôYÕ 30 U¦ úSWj§tÏ ùNnÕúU≠V©p Yôol× CÚm× RVô¬dLlTÓ¡\Õ.

Öi EÚiûP Yôol× CÚm× (Nodular castiron)

CÕ úU≠V©p Yôol× CÚm× úTôXúYCÚdÏm. B]ôp GkR ®RUô]ùYlTTR²ÓRÛm úRûY CpûX. ÖiEÚiûP Yôol× CÚm×, ùSôÓXo CÚm×PdûPp CÚm× vùToWônPp ¡WôlûTh(Spheroidal Graphite Iron) CÚm× GußmA±VlTÓ¡\Õ.

CÕ SpX ùU£²e RuûU, Yôol× ùNnÙmRuûU, úRnUô]jûR G§odÏm RuûU,Ïû\kR EÚÏ ¨ûX Utßm L¥]jRuûUEûPVÕ.

úU≠V©p Utßm Öi EÚiûP YôolûTTVuTÓj§ CVk§Wj§u TôLeLs RVôoùNnVlTÓ¡\Õ. A§L A[Ü CÝ®ûN UtßmSÓjRWUô] CmTôdh úXôÓ RôeLdá¥VTôLeLs RVôo ùNnVlTÓ¡\Õ. CÕ Ïû\kRùNX®p Yôol× ùNnVlTÓ¡\Õ. CÕ CÚm×Yôol©tÏ Uôt\ôÏm.

úR²Úm× (Wrought Iron) (RVô¬dÏm Øû\)(TPm 1)

CÚm©p Es[ L¯Ül ùTôÚhLû[ ¿d¡RVô¬dLlTÓm ÑjRUô] CÚm× úR²Úm×G]lTÓm. úR²ÚmûT TÏjRôp A§p 99.9®ÝdLôÓ CÚmTôÏm (TPm 1). úR²ÚmûTùYlTlTÓj§]ôp EÚLôÕ. B]ôp C[Ïm.Ck¨ûX«p CûR GkR Y¥Yj§Ûm úTôo_õÓùNnVØ¥Ùm.

SÅ] Øû\ûV TVuTÓj§ úR²ÚmûT ùT¬VA[®p EtTj§ ùNnVØ¥Ùm Øû\L[ôY]

– ×h≠e ùNnØû\ (puddling process)

– AvPôu (A ) ûTVov ùNnØû\(aston or Byers process)

G@Ï (Steel)

CÕ ÑjRUô] CÚm×, LôoTu A§LUôLCÚdÏm. LôoTu áÓRXôL CÚlTRôp CÕ



59

Eß§Vô]úRô CpûX. NôRôWQ Øû\«pCûR aôoPú]ô ApXÕ ùPmTúWôùNnVØ¥VôÕ. Sh, úTôph, ¬®h, RLÓ,JVo, T AVou Utßm Be¡p AVouØR≠VûYLs CR]ôp RVôoùNnVlTÓ¡\Õ.

B SÓjRW LôoTu G@Ï: 0.25 ØRp 0.5®ÝdLôÓ LôoTu Es[Õ. LôoTuA§LUôL CÚlTRôp ªÚÕ G@ûLLôh¥Ûm L¥]Uô]Õ Utßm§iûUVô]Õ Utßm ùP]ô£h¥ A§Lm.CûR L¥]jRuûU ApXÕ ùPmToùNnVXôm. úTôo_õe Utßm úWô≠e êXmTX®RUô] ùTôÚhLs RVôoùNnVlTÓ¡\Õ. A§L CÝ®ûN ùLôiP¥ël×Ls, JVoLs, ®YNôV LÚ®Ls,CûQl× WôÓLs, úLm`ôlh, vúT]oUtßm Ll©Ls úTôu\Ytû\ ùNnVTVuTÓjRlTÓ¡\Õ.

C A§LUô] A[Ü LôoTu Es[ G@Ï:C§p LôoTu A[Ü 0.5 ØRp 1.5 ®ÝdLôÓCÚdÏm. CÕ ªLÜm L¥]Uô]Õ UtßmÏû\kR úRnUô]m ùLôiPÕ. ùYlTTR²ÓRp êXm CûP L¥]UôdLXôm.CûR YôolúTô ApXÕ úWôpúXô ùNnVØ¥VôÕ. CÕ ªLÜm L¥]Uô]Õ,§iûUVô]Õ. CÕ ̈ ûXVô] LôkR Nd§ùLôiPÕ. áoûUVô] LÚ®Ls, v©¬e,LhX¬v, Tm×Ls, AWm, úLôpÓ £Np,©WvûP ØR≠V] CkR G@¡]ôp RVôoùNnVlTÓ¡\Õ.

2 LXl× G@Ï (Alloy Steel)≠ú]ô≠Vm, UôeLÉv, PevPu úTôu\EúXôLeLû[ G@ÏPu LXkÕ RVôoùNnVlTÓm EúXôLm LXl× G@Ï G]lTÓmCkR LXl× EúXôLj§u RuûULsêXlùTôÚhLû[ ùTôÚjRÕ.

LXl× G@¡u YûLLs

Ød¡VUô] CWiÓ YûL LXl× G@ÏLs:

A Ïû\kR LXl× G@Ï (Low alloy steel)

B A§L LXl× G@Ï (High alloy steel)

A Ïû\kR LXl× G@Ï: LôoTu R®W Ut\EúXôLeLs Ïû\kR A[®p CÚdÏm.C§p CÝ®ûN §\u A§LUôL Es[Õ.CûR ùYp¥e ùNnV CVÛm. CûRL¥]lTÓjRÜm Utßm ùPmTÚm ùNnVØ¥Ùm. ®Uô]j§u TôLeLs Utßm úLm`ôlh (cam shaft) úTôu\Ytû\ RVôo ùNnVTVuTÓjRlTÓ¡\Õ.

L¥]UôLÜm Utßm §iûUVôLÜm CÚdÏm.C§p 0.15 ØRp 1.5 ®ÝdLôÓ LôoTu LXkÕEs[Õ. C§p NpTo, TôvTWv úTôu\ Ut\úRûYVt\ ùTôÚhLÞm LXkÕ Es[Õ.B]ôp CûYLû[ R²VôL ©¬dL CVXôÕ.JÚ Ï±l©hP ùYlT ̈ ûX«p ùYlTlTÓj§AÕ GiùQn ApXÕ Ri½WôpÏ°o®dLlThÓ aôoPu Utßm ùPmToùNnVlTÓ¡u\Õ.

TXYûLVô] G@ÏLû[ RVô¬dL ̧ rLiPØû\Ls TVuTÓjRlTÓ¡u\].

1 £ùUiúPNu ùNnØû\(Cementation process)2 ÏÚ£×p ùNnØû\ (Crucible process)3 ùT£Uo ùNnØû\ (Bassemer process)4 KlTu ùaoj ùNnØû\ (Open hearth process)5 GXdhúWô ùRoúUô ùNnØû\ (Electro thermo

process)6 ûa ©¬dÏYu£ ùNnØû\ (High frequency

process)11 .13 G@¡u Ød¡VUô] YûLLs:

Ød¡VUô] CWiÓ YûL G@ÏLs

1 NôRôWQ G@Ï (Plain steel)2 AXôn G@Ï (Alloy steel)1 NôRôWQ G@Ï (Plain steel). C§p LôoTàm

CÚm×m LXkÕ CÚd¡u\Õ. LôoTu®ÝdLôÓdÏ HtT NôRôWQ G@Ï¸rLiPYôß ©¬dLlThÓs[Õ.

A Ïû\kR LôoTu G@Ï (Low carbon steel)B SÓjRW LôoTu G@Ï (Medium carbon steel)C A§LUô] A[Ü LôoTu Es[ G@Ï

(High carbon steel)A Ïû\kR LôoTu G@Ï: CÕ ªÚÕ G@Ï

Gußm AûZdLlTÓ¡\Õ. 0.15 ØRp 0.25®ÝdLôÓ LôoTu Es[Õ. CqYôßÏû\kR A[Ü LôoTu Es[RôpúRûYVô] A[®tÏ ªÚÕYôLEs[Rôp §¬×ûY (strain) RôeÏm úTôo_õeUtßm úWô≠e êXm TX Y¥YeL°pCûR AûUdL CVÛm. CÕ L¥]Uô]úRô,



60

B A§L LXl× G@Ï: LôoTu R®W Ut\EúXôLeLs úXô AXônv¼ûXdLôh¥Ûm A§L ®ÝdLôÓ LXkÕCÚdÏm. CÕ ̧ rLiPYôß YûLlTÓjRlThÓs[Õ.

a ûa vÀÓ v¼p (High Speed Steel):CÕ ûa PevPu AXôn v¼p GußmAûZdLlTÓm. Hù]u\ôp C§p A§LA[Ü PevPu LXkÕ Es[Õ. PevPuA[ûYl ùTôÚjÕ êuß YûLVôL©¬dLlThÓs[Õ.

1 PevPu 22%, ÏúWôªVm4%, Y]¥Vm 1%

2 PevPu 18%, ÏúWôªVm 4%, Y]¥Vm 1%

3 PevPu 14%, ÏúWôªVm 4%, Y]¥Vm 1%

C§p ùYhÓ LÚ®Ls ùNnVlTÓ¡\Õ.Hù]u\ôp CÕ ªLÜm L¥]Uô]Õ, B]ôpÏû\kR ¡¬h¥Lp ùYlTj§p ªÚÕ RuûUAûPÙm. ùYhÓm LÚ® ùNVpTÓm ùTôÝÕùYlTm A§L¬jRôp, ùYhÓm LÚ®TV]t\Rô¡®Óm. úUÛm úYûX ùNnÙmRÏ§ûV CZkÕ ®Ó¡\Õ. B]ôp A§L®ÝdLôÓ PevPu CÚlTRôp, A§LùYlTj§Ûm CÕ úYûX ùNnÙm.ùYhÓdLÚ®, ¥¬pv, LhPo, ÃUo, BdNô©ú[Ó ØR≠V]Ytû\ ùNnV TVuTÓ¡\Õ.

b ¨dLp v¼p (Nickel Steel):C§p LôoTu 3 ®ÝdLôÓ, ¨dLp 0.25 ØRp0.35 ®ÝdLôÓ Es[Õ. ¨dLp LXkÕCÚlTRôp CÝ®ûN,Áh£«Vp GpûXUtßm L¥]jRuûU A§L¬d¡u\Õ. CÕÕÚl©¥dLôÕ. 0.35 ®ÝdLôÓ ¨dLp LXkÕEs[Rôp, ùYhÓm §\u NôRôWQ LôoTuv¼ûXd Lôh¥Ûm 6 UPeÏ A§Lm. ¬®h,ûTl, Bd£p, ̀ ôlh úTÚkÕL°u TôLeLsUtßm ®Uô]eLs B¡VûYLû[ RVôoùNnV TVuTÓjRlTÓ¡\Õ. 5 ®ÝdLôÓúLôTôph, 30 ØRp 35 ®ÝdLôÓ ̈ dLÛPuLXdÏm ùTôÝÕ CuYôo v¼p -BLUôß¡u\Õ. Ød¡VUôL ®ûX EVokRLÚ®Ls RVô¬dL TVuTÓjRlTÓ¡\Õ.

c Y]¥Vm v¼p (Vanadium Steel):C§p 1.5 ®ÝdLôÓ LôoTu, 12.5 ®ÝdLôÓPevPu, ÏúWôªVm 4.5 ®ÝdLôÓ, Y]¥Vm5 ®ÝdLôÓ Utßm úLôTôph 5 ®ÝdLôÓLXkÕ CÚdÏm. CRu Áh£«Vp GpûX,CÝ®ûN Utßm Pd¥≠h¥ A§Lm CÚdÏm.`ôol A§oûY RôeÏm YpXûU Es[Õ.Ød¡VUôL LÚ®Ls RVô¬dL TVuTÓjRlTÓ¡\Õ.

d UôeLÉv v¼p (Manganese Steel):CÕÜm vùTNp ûa AXôn v¼p GußAûZdLlTÓ¡\Õ. C§p 1.6 ØRp 1.9®ÝdLôÓ UôeLÉÑm Utßm 0.4 ØRp 0.5®ÝdLôÓ LôoTàm LXkÕ Es[Õ. CÕL¥]Uô]Õ Utßm Ïû\kR úRnUô]mEûPVÕ. LôkRjRôp Tô§dLôÕ CÕ¡ûWiPo Utßm W«p Tô«ihL°pTVuTÓjRlTÓ¡\Õ.

e vùP«uùXv v¼p (Stainless Steel):CÕ CÚmúTôÓ 0.2 ØRp 90.6 ®ÝdLôÓLôoTu, 12 ØRp 18 ®ÝdLôÓ ÏúWôªVm, 8®ÝdLôÓ ¨dLp, 2 ®ÝdLôÓ Uô≠l¥]m(molybdenum) LXkÕ Es[Õ. Lj§Ls, Lj§¬dúLôpLs, Tôj§WeLs, ®Uô] TôLeLs,JVo, ûTl×Ls Utßm ¡VoLs úTôu\Ytû\RVô¬dL TVu TÓjRlTÓ¡\Õ.

vùP«uùXv v¼≠u RuûULs(Properties of stainless steel):1 A§L A¬Uô] G§ol×jRuûU

2 A§L LÓeÏ°o §iûUjRuûU

3 A§L L¥]UôdÏm RuûU

4 A§L ùYlTjRôeÏ §\u

5 A§L RLPôL ¿Þm RuûU

6 A§L RôeÏ¡\u Utßm L¥]j RuûU

7 SuÏ LYÚm úRôt\m

8 Ïû\kR TWôU¬l×

f £≠Lôu v¼p (Silicon Steel):C§p 15 ®ÝdLôÓ £≠dLôu Es[Õ,£≠dLôu A[ûYl ùTôßjÕ TpúYß YûLCÚm×f NjÕs[ EúXôLj§p TVuTÓjRlTÓ¡\Õ. 0.5 ®ÝdLôÓ ØRp 1 ®ÝdLôÓ£≠dLôu 0.7 ®ÝdLôÓ ØRp 0.95 ®ÝdLôÓUôeLÉÑ LXkÕ LhÓUô] úYûXLÞdÏTVuTÓjRlTÓ¡\Õ. 2.5 ØRp 4 ®ÝdLôÓ£≠dLôu LXûY êXm ªuNôWúUôhPôoù_]úWhPo, ¥WôuvTôoUÚdLô] úXªú]Nu B¡VûYLsEtTj§ ùNnVlTÓ¡u\]. WNôV]ùRô¯tNôûX«p 14 ®ÝdLôÓ £≠dLôuLXûY TVuTÓjRlTÓ¡\Õ.

g úLôTôph v¼p (Cobalt Steel):ûa LôoTu v¼≠p 5 ØRp 35 ®ÝdLôÓúLôTôph LXkÕ Es[Õ CRu §iûUjRuûU Utßm ùP]ô£h¥ (Toughness andtenacity) A§Lm. CRtÏ LôkR Nd§ EiÓ,AR]ôp ¨ûXVô] LôkRm EÚYôdÏYRtÏTVuTÓjRlTÓ¡\Õ.



61

CÚm×fNjÕs[ Utßm CÚm×fNj§pXôR EúXôL YûLLs T«t£ 1.7.21

CÚm×fNjÕs[ Utßm CÚm×fNj§pXôR LXl× EúXôLeLs

CÚm×fNjÕs[ LXl× EúXôLm UtßmARàPu LXdÏm EúXôLeLs (Alloyingmetals and ferrous alloys)

CWiÓ (A ) CWiÓdÏ úUtThPEúXôLeLû[ EÚd¡ EÚYôd¡]ôp LXl×EúXôLm ¡ûPdÏm.

CÚm×fNjÕs[ EúXôLeLs Utßm LXl×EúXôLeLÞdÏ ªL Ød¡VUô] EúXôLmCÚm× BÏm. EÚd¡ CûQdÏmEúXôLj§u TeÏ Utßm YûL B¡VYtû\lùTôÚjÕ LXl× G@¡u RuûU UôßTÓm.

AXôn v¼p RVôôõdL ùTôÕYôLTVuTÓjRlTÓm EúXôLeLs

¨dLp (Ni) (Nickel)

CÚ JÚ L¥]Uô] EúXôLm. TX YûLVô]A¬Uô]eLû[ G§ôódÏm RuûUÙûPVÕ.

CÚ ùRô¯tNôûX«p EtTj§«p, ARôYÕ¨dLp, LôhªVm úThPôõLs, TônXôó ¥ël,CuPôó]p LmTvPu CVk§Wj§uYôpÜLs, CVk§Wj§u vTôôód ©[dÏLsØR≠V] RVô¬dL TVuTÓ¡\Õ. ¨dL≠uEÚÏ ¨ûX 1450°C. ¨dLÛdÏ LôkR RuûUEiPôdLXôm. ¨ûXVô] LôkR Nd§EiPôdL ©Wj§úVLUôL ̈ dLp v¼p AXônTVuTÓ¡\Õ. ªu ØXôm éÑYRtÏ ¨dLpTVuTÓjRlTÓ¡\Õ. CuYôôó v¼≠p 36®ÝdLôÓ ¨dLp Es[Õ. CÕ L¥]Uô]ÕUtßm A¬Uô]j§tÏ G§Wô]Õ. CuYôôóv¼p êXm ®ûX EVôókR LÚ®Ls RVôôóùNnVlTÓ¡\Õ, Hù]u\ôp CuYôôóv¼ÛdÏ ¿[ ùTÚdÏ Gi ªLÜm Ïû\Ü.

¨dLp þv¼p LXl× EúXôLj§p, ¨dLp 2ØRp 50®ÝdLôÓ LXkÕ Es[Õ.

ÏúWôªVm (Cr) (Chromium)

ÏúWôªVjûR G@ÏPu úNôójRôp AÕÕÚ©¥lTûR RÓdÏm, L¥]jRuûU Utßmv¼≠u Eß§ A§LôõdÏm. 30 ®ÝdLôÓÏúWôªVm Es[ ÏúWôªVm v¼p¡ûPd¡u\Õ.

ÏúWôªVjÕPu, ¨dLp, PevPu UtßmUô≠l¥]m LXdLlTÓYRu êXmRô²Ve¡L°u TôLeLs Utßm Lh¥eåpLs RVôôõdLlTÓ¡\Õ.

TôLeLû[ ªu ØXôm éÑYRtÏ, ÏúWôªVmTVuTÓ¡\Õ. £≠iP¬u ûXu]ôõuEhTÏ§«p ÏúWômþ©ú[h ùNnVlTÓ¡\Õ.CR]ôp úRnUô]jûR G§ôódÏm Bt\pA§Lôõd¡\Õ. vGP«uùXv v¼≠p 13®ÝdLôÓ ÏúWôªVm Es[Õ. ÏúWôªVm¨dLp v¼p, úTôõe ùNnV TVuTÓ¡\Õ.ûLdLÚ®Ls ARôYÕ vTô]ôóLs UtßmôõgNv (wrenches) B¡VûYLs RVô¬dLÏúWôªVmþY]¥Vm v¼p ETúVôLlTÓjRlTÓ¡\Õ.

UôeLÉÑ (Mn) (Manganese)

v¼ÛPu UôeLÉûN úNô ójRôpL¥]jRuûUÙm, Eß§Ùm A§Lôõd¡u\Õ.B]ôp Ï°ôóf£ ¨ûX Ïû\¡u\Õ.

LÚ®L°u ×\lTWlûT L¥]lTÓj§úRnUô]jûR Ïû\dL UôeLÉÑTVuTÓjRlTÓ¡\Õ. 14 ®ÝdLôÓ ùLôiPUôeLÉÑ v¼p, ®YNôVm NmTkRlThPLÚ®Ls ùNnV ARôYÕ EZÜ LÚ®Ls Utßm©ú[ÓLs ùNnV TVuTÓjRlTÓ¡\Õ.

£≠dLôu (Si) (Silicon)

v¼ÛPu £≠dLôû] úNôójRôp, A§LùYlTjRôp Bd£úPNu HtTÓYûR RÓdÏmNd§ v¼ÛdÏ A§Lôõd¡u\Õ. CR]ôpÁh£Vp RuûU A§LôõdÏm UtßmÕÚ©¥lTûR RÓdÏm. v©ôõe Utßm£XYûLVô] v¼pLs ÕÚ©¥dLôUp CÚdL£≠dLôu LXl× G@Ï TVuTÓjRlTÓ¡\Õ.

Yôôól× CÚm©p 2.5% ®ÝdLôÓ £≠dLôuLXkÕ Es[Õ. CÕ ¡WôlûTh EÚYôLERÜ¡\Õ. CRu LôWQUôL Yôôól× CÚm©uùU£u ùNnVlTÓm RuûU A§L¬d¡\Õ.

PevPu (W) (Tungsten)

PevP²u EÚÏ ¨ûX 3380° C CûR ªLùUp≠V Lm©VôL ùNnV Ø¥Ùm.

CdLôWQjRôp ªuNôW ®[dÏL°u©≠ùUuPôL TVuTÓ¡\Õ.


62

A§L úYL ùYhÓm LÚ® RVôôó ùNnVPevPu LXl× EúXôLm TVuTÓ¡\Õ.PevPu 18 ®ÝdLôÓ, ÏúWôªVm 4®ÝdLôÓ Utßm Y]¥Vm JÚ YõÝdLôÓA[®p A§úYL v¼p AXô«p Es[Õ.

vùPpûXh Gu\ AXô«p ÏúWôªVm 30®ÝdLôÓ, PevPu 20 ®ÝdLôÓ,LôôóTu 1ØRp 4 ®ÝdLôÓ ªÏ§ úLôTôph LXkÕCÚdÏm.

Y]¥Vm (Va) (Vanadium)

CÕ v¼≠u L¥]jRuûUûVA§Lôõd¡u\Õ. ¡Vôó, LÚ®Ls ØR≠VûYY]¥Vm v¼p êXm RVôôó ùNnVlTÓ¡\Õ.v¼p LÚ®Lû[ ªL úSôój§Vô] ÕLsLhPûUl©p (fine grain) RVôôõdL Y]¥VmTVuTÓ¡\Õ.

ÏúWôm Y]¥Vm v¼≠p, ÏúWôªVm 0.5ØRp 1.5 ®ÝdLôÓ, Y]¥Vm 0.15 ØRp 0.3®ÝdLôÓ LôôóTu 0.13 ØRp 1.10 ®ÝdLôÓLXkÕ CÚdÏm.

CkR AXôn, A§LUô] CÝ®ûNûVdùLôiPÕ, Áh£«Vp GpûX, UtßmPd¥≠h¥ ùLôiPÕ. CkR AXôûVTVuTÓj§, v©ôõe ¡Vôó, ̀ ôlh Utßm ¥WôlúTôôó_õÓ TôLeLs RVôôóùNnVlTÓ¡\Õ.

Y]¥Vm ûa vÀÓ v¼≠p LôôóTu 0.70®ÝdLôÓ, Y]¥Vm 10 ®ÝdLôÓ Es[Õ.CqYôß AûUkÕ CÚkRôp AÕ EVôóókRûavÀÓ v¼p G]lTÓm.

úLôTôph (Co) (Cobalt)

úLôTôp¥u EÚÏ ¨ûX 1495°C. CÕLôkRjRuûUûV ¨ûX ¨ßj§d ùLôsÞm.ªÏkR ùYlT ¨ûX«Ûm úRnUô]jûRG§ôódÏm RuûU EûPVÕ. áôóûUVô]ùYhÓ Øû]ûV EûPV LÚ®Ls, TôpúTôõev, LôkRm úTôu\Ytû\ RVôôõdLúLôTôph TVuTÓ¡\Õ. úLôTôphûavÀhv¼p (£X NUVeL°p ãlTôó H.S.S.G]lTÓm) C§p 5 ØRp 8 ®ÝdLôÓúLôTôph CÚdÏm. 18 ®ÝdLôÓ PevPuH.S.S. I Lôh¥Ûm C§p L¥]jRuûUÙmúRnUô] G§ol×j RuûUÙm A§Lm.

úUô≠l¥]m (Mo) (Molybedenum)

CRu EÚÏ¨ûX 2620°C. ùYlTlTÓjÕmùTôÝÕ ªÚÕ RuûUdÏ G§WôLùNVpTÓ¡\Õ. úUô≠l¥]m ûavÀh

v¼≠p 6 ®ÝdLôÓ úUô≠l¥]m, 6 ®ÝdLôÓPevPu, 4 ®ÝdLôÓ ÏúWôªVm Utßm 2®ÝdLôÓ Y]¥Vm Es[Õ. CqYûL v¼pªLÜm L¥] RuûUÙm Utßm SpX ùYhÓRuûUÙm ùLôiPÕ.

LôhªVm (cd) (Cadmium)

LôhªVj§u EÚÏ ¨ûX 320°C. v¼pTôLeLÞdÏ úUtéfÑ éN TVuTÓ¡\Õ.

CÚm×fNj§pXôR LXl× EúXôLeLsUtßm ARàPu LXdÏm EúXôLeLs

CÚm× Nj§pXôR EúXôLeLs UtßmLXl× EúXôLeLs

ùNm× Utßm ARu LXl× EúXôLeLs

CÚm× NjÕ CpXôR EúXôLm Sôu ùTôóWvEúXôLm G] AûZdLlTÓ¡\Õ. ERôWQmùNm×, AÛª²Vm. ÕjR SôLm LôÃVm UtßmùYsÇVm.

ùNm× (Copper)

UôXûNh Gu\ RôÕ®p CÚkÕ ùNm×RVôôóùNnVlTÓ¡\Õ. C§p 55 ®ÝdLôÓùNm×m Utßm ûTûWhv C§p 32 ®ÝdLôÓùNm× LXkÕ CÚdÏm.

RuûULs (Properties)

ùNmùTôu ̈ \m. CRu ̈ \jûR ûYjÕ G°§pA±VXôm.

AûUlûT ©[ÜTÓj§]ôp ¡WôàXôLúRôußm. CûR úTôôó_ó ApXÕ úWôpÓùNnRôp CÕ ûTTôó BL úRôußm.

C§p PdûPp Utßm úUp≠VTp RuûUA§Lm. AR]ôp CûR RLPôLúYô ApXÕLm©VôLúYô Uôt\Xôm.

ªuNôWjûR G°§p LPjÕm ùNmûTTVuTÓj§ ªuNôW úL©s Utßm ªuNôR]LÚ®L°u TôLeLs RVôôó ùNnVlTÓ¡\Õ.CûYLs ªuNôWjûR LPjR TVuTÓjRlTÓ¡\Õ.

ùNm× JÚ SpX ùYlTd LPj§,ÕÚl©¥lTûR G§ôódÏm. CRu LôWQUôLùLô§LXu ùSÚl×ùTh¥, Ri½ûWùYlTlTÓjÕm LÚ®Ls, CWNôV]ùRô¯tNôûXLs Utßm Y¥lTôûXL°pRi½o ÏZônLs Utßm LXuLs TVuTôh¥p ETúVôLlTÓjRlTÓ¡\Õ. úUÛmNôpP¬e AV¬u RVô¬dL TVuTÓjRlTÓ¡\Õ.



63

ùNm©u EÚÏ ¨ûX 1083o C.

úaUôõe ApXÕ úWô≠e ùNnÕ ùNm©uCÝ®ûNûV A§L¬dLXôm.

ùNm×LXl× EúXôLm (Copper Alloys)

©jRû[ (Brass)

©jRû[,ùNmûTÙm ÕjRSôLjûRÙm LXkÕùNnVlTÓm Kôó AXôn BÏm. £X YûL©jRû[Ls, £±R[Ü ùYsÇVm ApXÕLôÃVm LXkÕ ùNnVlTÓ¡\Õ. ApXô«uêXlùTôÚ°u ®ÝdLôhûP ùTôÚjÕ©jRû[«u ¨\m AûUÙm. CRu ¨\mUgNs ApXÕ CúXNô] UgNs ApXÕùYiûUVôL CÚdÏm. G°§p ùU£²eùNnVXôm, ©jRû[A¬Uô]jûR G§odÏmRuûUÙûPVÕ.

úUôhPôó Lôôõu úW¥úVhPôó úLôôó UtßmRi½ôó ÏZônLs ØR≠V] ùNnYRtÏ A§LA[®p ©jRû[ TVuTÓjRlTÓ¡\Õ. CÕúUÛm L¥]UôL úNôpPôõe ©úW£e êXmúLv Tt\ûYl× B¡VYt±tÏ TVuTÓ¡\Õ.©jRû[«u EÚÏ ̈ ûX 880 ØRp 930oC. YûWCÚdÏm.

TX®R ®¡ReL°p ©jRû[ RVôôó ùNnÕA§p TpúYß ETLWQeLs RVôô óùNnVlTÓ¡\Õ.

ùYiLXm (Bronze)

ùNmûTÙm, ùYsÂjûRÙm LXkÕùNnVlTÓm JÚ LXl× EúXôLm BÏm. £XNUVm ARàPu ÕjR SôLjûRÙm úNôójÕ®ú``Uô] RuûU EiPôdLlTÓ¡\Õ.

CRu ̈ \m £Ll× ØRp UgNs YûW AûUkÕCÚdÏm. CRu EÚÏ ¨ûX 1005oC. CÕ©jRû[ûV ®P L¥]Uô] EúXôLm. CûRªL áôóûUVô] LÚ®L°u êXm ÑXTUôLùU£²e ùNnV Ø¥Ùm. CRu ÕLsLs¡WôàXWôL CÚdÏm. ©Wj§úVLUô]ùYiLX AXôûV TVuTÓj§ ©úW£e WôhùNnVlTÓ¡\Õ. TpúYß LXûY ®¡Rj§pRVô¬dLlTÓm ùYiLXm TpúYßùTôÚsLs RVôôó ùNnV TVuTÓjRlTÓ¡\Õ.

LôÃVm Utßm ARu LXl× EúXôLeLs(Lead and its alloys)

LôÃVm CÚm×fNj§pXôR EúXôLj§pùTôÕYôL TVuTÓm EúXôLm BÏm.ùRô¯tNôûX«p TpúYß ®RUô]TVuTôh¥tÏ ETúVôLlTÓjRlTÓ¡\Õ.

LÄ]ô (Galena) Gu\ êXlùTôÚ°≠ÚkÕLôÃVm RôVôôó ùNnVlTÓ¡\Õ. LôÃVmL]UôL EúXôLm BÏm. CûREÚdÏmùTôÝÕ ùYs°ûV úTôußúRôt\m A°dÏm. CÕ ªÚÕYô]Õ UtßmúUp≠V©p RuûU ùLôiPÕ.A¬Uô]j§tÏ G§Wô]Õ. ¨ëdÏXôôóúWPVúN²p SpX CuÑúXhPWôLTVuTÓ¡\Õ. Npéôõd B£h UtßmûahúWô Ïú[ôôõd B£h úTôu\B£hLû[ G§ôódÏm RuûU ùLôiPÕ.

CÕ Lôôó úThPôõ«p TVuTÓjRlTÓ¡\Õ.úNôpPôó RVôôó ùNnV TVuTÓ¡\Õ. úUÛmCRu êXm ùT«ih RVôôó ùNnVlTÓ¡\Õ.

LôÃV AXônLs (Lead Alloys)

úT©h EúXôLm (Babbit metal)

úT©h EúXôLm LôÃVm, ùYsÇVm, ùNm×,Utßm Bi¥U¦«u LXlTôÏm. CÕªÚÕYô]Õ, EWônûY RÓdÏm. AR]ôXóCÕ úTôõe RVô¬dL TVuTÓjRlTÓ¡\Õ.

DVm Utßm ùYsÇVm LXl©p NôlhúNôpPo RVôo ùNnVlTÓ¡\Õ.

ÕjRSôLm Utßm ARàûPV AXônLs(Zinc and its alloys)

RLÓLs ÕÚ©¥dLôUp CÚdL ARu ÁÕÕjRSôL éfÑ ùTôÕYôL éNlTÓ¡\Õ.ERôWQj§tÏ CÚm× Yô°, ÕjRSôL áûWRLÓLs ØR≠V].

LôXûUu ApXÕ ©[ih Gu\êXlùTôÚs êXm ÕjRSôLm ¡ûPd¡\Õ.

CRu EÚÏ ¨ûX 420o C.

CÕ EûPVdá¥VÕ. ùYlTlTÓj§]ôpC[Ïm. CÕ úUÛm A¬Uô]j§tÏG§Wô]Õ. CjRuûU«u LôWQUôL úThPôõùLôsLXeLs RVôôó ùNnV Utßm áûWRLÓLÞdÏ úUtéfÑ éN TVuTÓjRlTÓ¡\Õ.

LôpYû]v ùNnVlThP CÚm×j RLÓLsÁÕ ÕjRSôLm éNlTÓ¡u\].



64

ùYsÇVm Utßm ùYsÇV AXônLs(Tin and tin alloys)

ùYsÇVm (Tin)

Lô£hûWh (cassiterite) ApXÕ ¥u vúPôu(tinstone) êXm ùYsÇVm RVôoùNnVlTÓ¡\Õ úRôt\j§p ùYs° úTôußùYiûUVôL CÚdÏm Utßm CRàûPVEÚÏ ¨ûX 231o C. CÕ ªLÜm ªÚÕYô]ÕUtßm A§L A[Ü A¬Uô] G§ol×j RuûUùLôiPÕ.

EQÜ AûPdÏm CÚm× ¥uL°p úUpéfNôL TVuTÓ¡\Õ. úYß EúXôLeLÞPuLXkÕ AXôn RVôo ùNnVÜmTVuTÓjRlTÓ¡\Õ.

ERôWQm: ùYsÇVØm ùNm×m úNojRôpùYiLXm EÚYô¡\Õ, ùYsÇVØm DVØmúNojRôp úNôpPo (solder) EÚYôÏm.ùYsÇVm, ùNm×, DVm Utßm Bi¥U¦B¡VûYLû[ úNojÕ Tô©h EúXôLm (Babbit)RVôo ùNnVlTÓ¡\Õ.

AÛª²Vm (Aluminium)

AÛª²Vm JÚ Sôu ùToWv EúXôLm BÏm.CÕ TôdûNh (BAUXITE) Gu\ RôÕ ùTôÚ°pCÚkÕ RVôo ùNnVlTÓ¡\Õ. CÕ ùYsû[ApXÕ NômTp ̈ \m ùLôiPRôL CÚdÏm.CRu EÚÏ ̈ ûX 660o C. CÕ ªuNôWm Ut\mùYlTjûR G°§p LPjÕm RuûU EûPVÕ.CÕ ªÚÕYô]Õ, Utßm PdûPp (Ductile)RuûU ùLôiPÕ Ïû\kR CÝ®ûNùLôiPÕ, CÕ ®Uô]m EtTj§, UtßmúTl¬úL`u úYûX (Fabrication) B¡VCPeL°p TVuTÓjRlTÓ¡\Õ, Hù]u\ôpCÕ ªLÜm CúXNô] EúXôLm BÏm ªuùRô¯XLeL°Ûm RtùTôÝÕ A§L A[®pTVuTÓjRlTÓ¡\Õ. ÅÓL°ÛmùYlTlTÓjRdá¥V ùTôÚsL°pTVuTÓjRlTÓ¡\Õ.



65

CÚm©tÏm, G@¡tÏm CûPúVVô] ®j§VôNeLs, LXl× G@Ï UtßmLôoTu G@Ï T«t£ 1.7.22

CÚm©tÏm, G@¡tÏm CûPúVVô] ®j§VôNeLs (Difference between iron and steel)

1 PôhPô AVou v¼p Àaôo

2 Ck§Vu AVou v¼p úU,YeLô[m

3 ®vúYvYWnVô LoSôPLôAVou v¼p

4 ©Xôn v¼p ©[ôuh Nj¾vLo

5 ÕoLôléo v¼p úU.YeLô[m©[ôuh

6 ApXôn v¼p úU.YeLô[m©[ôuh (ÕoLôéo)

7 ùTôdLôúWô v¼p Àaôo©[ôuh

8 ÚoúLXô v¼p J¬Nô©[ôuh

9 úNXm v¼p ©[ôuh RªrSôÓ

10 ®NôLlTh¥]m v¼p Bk§W©[ôuh ©WúRNm

Ck§Vô®pEs[CÚm× ùRô¯t NôûXLs

Y. CÚm× ùRô¯t Uô¨Xm Gi NôûX«u ùTVo

Y.Gi A¥lTûP CÚm× G@ÏúYßTôÓLs

1 AûUl× çV¨ûX CÚm× Utßm LôoTu B¡VYt\ôpEÚYô]Õ.

2 YûLLs Yôol× CÚm× LôoTu G@Ï Utßm LXl× G@ÏúR²Úm× Utßm G@Ï

3 ÕÚl©¥jRp G°§p Bd³úPNu TpúYß áßLs Es[RôpAûPRp Utßm ARu ÕÚl©¥jR≠ÚkÕ TôÕLôd¡\Õ.®û[YôL ÕÚl©¥lTÕ

4 ×\júRôt\m ÕÚl©¥jÕm, ùNôW T[T[lTôL CÚdÏm.ùNôWlTôLÜm CÚdÏm

5 ETúVôLm Lh¥PeLs, LÚ®Ls Lh¥PeLs, LôoLs, W«púYUtßm Rô²Ve¡L°p Utßm Rô²Ve¡L°p

6 ¡ûPjRp CVtûL«p ¡ûPd¡\Õ EÚYôdLlTP úYiÓm.

1 CÚm× NjÕ A§Lm C§p CÚm× NjÕ ¡ûPVôÕ

2 CRu EÚÏ ̈ ûX EÚÏ ̈ ûX Ïû\ÜA§Lm

3 CRu ̈ \m LÚl× CÕ TpúYß ̈ \eL°pApXÕ ©WÜu CÚdÏm

4 ÕÚ ©¥dÏm ÕÚ ©¥dLôÕ

5 LôkRjRuûUûV LôkRjRuûUûV HtTÓjR Ø¥Ùm HtTÓjR Ø¥VôÕ

6 Ï°okR ̈ ûX«p CÕ ùYlT ̈ ûX«pùSôßeÏm RuûU ùSôßeÏm RuûUùLôiPÕ ùLôiPÕ

CÚm×fNjÕs[ CÚm×fNj§pXôREúXôLm EúXôLm

1 LôoTu A§Lm LôoTu Ïû\Ü

2 LôoTu R²jÕ CÚdÏm LôoTu LXkÕ CÚdÏm

3 EÚÏ ̈ ûX Ïû\Ü EÚÏ ̈ ûX A§Lm

4 LôkR RuûUûV LôkR RuûU HtTÓjRHtTÓjR Ø¥VôÕ Ø¥Ùm

5 ùSôßeÏm RuûU CûR úTôo_ó ùNnVEs[Rôp CûRúTôo_ó Ø¥ÙmùNnVØ¥VôÕ

6 G°§p ÕÚ ©¥dLôÕ G°§p ÕÚ ©¥dÏm

7 CûR ùYpÓ CûR ùYpÓ ùNnVùNnVØ¥VôÕ Ø¥Ùm

Yôol× CÚm×dÏm G@ÏdÏm Es[ ®j§VôNm

Yôol× CÚm× G@Ï


66

Yôôól× CÚm×, ªÚÕ G@Ï, Utßm G@Ï B¡VYt±u RuûULû[ Jl©ÓRp(Comparison of the Properties of Cast Iron, Mild Steel and steel)

êXl 2 ØRp 4.5% LôôóTu 0.1 ØRp 0.25% LôôóTu 0.5 ØRp 1.7% LôôóTuùTôÚhLs(Composition)TXm (Strength) – CßdÏ ®ûN A§Lm – CßdÏ ®ûN – CßdÏ®ûN

SÓjRWUô]Õ A§Lm– CÝ ®ûN Ïû\Ü – CÝ ®ûN – CÝ ®ûN A§Lm

SÓjRWUô]Õ– ùYhÓ ®ûN Ïû\Ü – ùYhÓ ®ûN A§Lm – ùYhÓ®ûN A§Lm

úUp≠V©≠h¥ Ïû\Ü A§Lm A§Lm (malleability)

Pd¥≠h¥ Ïû\Ü A§Lm A§Lm (ductility)

L¥]jRuûU SÓjRWUô] L¥]j ªÚÕjRuûU L¥]jRuûU (hardness) RuûU Utßm L¥]j

RuûUdLô] ùYlTA[®tÏ ùYlTlTÓjRlThÓ L¥]lTÓjRlThÓ ÏûYuf (Quench)ùNnVlTÓ¡\Õ

§iûUj RuûU Ïû\Yô] §iûUj §iûUjRuûU LôôóTu A[ûYl(toughness) RuûU A§LUôL CÚdÏm ùTôÚjÕ §iûUj

RuûU UôßTÓm

ùSôßeÏm ùSôßeÏm úUp≠V©p úUp≠V©pRuûU (Brittleness)úTôôó_õV©≠h¥ úTôôó_ó ùNnV CVXôÕ úTôôó_ó ùNnV Ø¥Ùm úTôôó_ó ùNnV Ø¥Ùm(Forgeability)ùYpP©≠h¥ ÑXTUôL Tt\ ûYdL ÑXTUôL Tt\ ûYdL Tt\ ûYdLXôm

(Weldability) Ø¥VôÕ Ø¥Ùm

Yôôól× ÑXTUôL Yôôól× ÑXTUôL Yôôól× Yôôól× ùNnV(Casting) ùNnV Ø¥Ùm ùNnV CVXôÕ Ø¥Ùm

Áh£VpRuûU Ïû\Ü A§Lm A§Lm(Elasticity)

RuûULs Yôôól× CÚm× ªÚÕ G@Ï G@Ï

EúXôLm Utßm AúXôLj§u úYßTôÓLs

EúXôLm AúXôLm

T[T[lTôL T[T[lTôLCÚdÏm CÚdLôÕ

ªuNôWjûRÙm ªuNôWjûRÙmùYlTjûRÙm ùYlTjûRÙmSu\ôL LPjÕm G°§p LPjRd á¥VûY

ApX

ùTÚmTôÛm PdûPp RuûUPdûPp RuûU ¡ûPVôÕEûPVÕ

J° FÓÚYôÕ ùUp≠V RLPôLCÚkRôp J° FÓÚÜm

úUp≠V©p RuûU §PlùTôÚ[ôLA§Lm CÚdÏmùTôÝÕ

EûPkÕ®Óm

ApLûXu A£¥d BdûNPôLBdûNPôLUôßm Uôßm

J≠ GÝlTd á¥VÕ J≠ GÝlTôÕ(U¦ûV A¥dÏmùTôÝÕ HtTÓmJ≠ûVl úTôp)

ùTôÕYôL 1 ---- --- 3 ùTôÕYôL 4 ----- - - 8úYXu£ GXdhWôu úYXu£ GXdhWôuùLôiPÕ ùLôiPÕ

ùTÚmTôÛmÑXTUôL ÕÚ©¥dÏm

ùTôÕYôL EÚÏ ̈ ûXA§Lm(ùTôÕYôL §PlùTôÚs Aû\«uùYlT ̈ ûX«p(TôRWNm R®W)



67

CWlTo, UWm Utßm CuÑúXh¥e ùTôÚsLÞdLô] RuûULs UtßmETúVôLeLs T«t£ 1.7.23

CWlT¬u RuûULs UtßmETúVôLeLs (Properties and uses of rubber)

WlTo (Rubber)

CÕ Áh£j RuûUÙûPV ùTôÚ[ôÏm. CûRCqYô\ôL YûLlTÓjRXôm.

• CVtûL WlTo

• L¥] WlTo

• ùNVtûL WlTo

CVtûL WlTo (Natural rubber)

CÕ RôYWeLû[ ©¬jùRÓjRp êXm¡ûPd¡\Õ. ùYlTlTÓjÕmùTôÝÕC[Ïm. CÕ, 30°C -p. JhÓm RuûUÙPàm,5°C -p. L¥]UôÏm RuûU ùLôi¥ÚdÏm.

NpTo WlTÚPu úNodLlThÓ AkR áhÓlùTôÚs ùYlTlTÓjRlTÓ¡\Õ. CkRùNVpØû\ûV YpLû]£e GußAûZd¡ú\ôm. CkR ùNVp Øû\«u êXmY≠ûUVô], L¥]Uô] Utßm A§L¨ûXjRuûUÙûPV WlTo ¡ûPdÏm. úUÛmùYlT Uôt\j§]ôp Tô§dLlTPôUÛmUtßm BoLô²d LûWN≠p LûWVôUÛmCÚdÏm. ARu RhT ùYlTj RuûUûVA§L¬lTRu LôWQUôL Bd£úPNu ªLÜmÏû\dLlThÓ ®Ó¡\Õ.

LÚl× LôoTu, B«p ùUÝÏ UtßmTXYtû\ úNolTRu êXm EÚYUôt\mHtTÓjÕm RuûULs Ïû\dLlTÓ¡\Õ.WlTo DWj RuûUûV RôeLd á¥VÕ Utßmªu LPjRÛdÏ G§Wô] SpX RuûULsùLôiPÕ. CRu Ød¡Vj ¾ûULs ¸úZùLôÓdLlThÓs[Õ.

• ùThúWô≠Vm GiûQdÏ G§Wô] Ïû\kRRûP Es[Õ.

• ã¬V J° TÓmT¥ ûYdLd áPôÕ.

• A§L ªu AÝjRØs[ LPj§L°pCuÑúXN]ôL TVuTÓjRd áPôÕ.

• Ïû\kR ùYlT¨ûX ùNVp Øû\L°pTVuTÓj§]ôp, AÕ 60°C ùYlT¨ûX«pùY¥l× HtTÓRp Utßm EûPRp HtTÓm.

• ùNm×Pu, WlT¬p Es[ NpTo úY§®û] ×¬YRôp TVuTÓjÕm ùNm×d Lm©ùYsÇVm éNlTh¥ÚdL úYiÓm.

L¥] WlTo (Hard rubber)

NpT¬u A[®û] WlT¬p A§L¬lTÕUtßm ¿iP úSWm YpLû]£e ùNnYÕB¡VYt\ôp WlTo, L¥] WlTo BLUô±®Óm. CRû] GúTôû]h GußmAûZd¡ú\ôm. CÕ SpX ªu Lôl× RuûUUtßm CVk§W®Vp RuûU EûPVRôLCÚdÏm.

ETúVôLeLs (Uses)

CÕ úThP¬ LuùPn]oLs, úT]púTôoÓLs, ×xμe, GúTôû]h ¥ë×LsUtßm TXYtû\ RVô¬dLl TVuTÓ¡\Õ.

ùNVtûL WlTo (Synthetic rubber)

CÕ CVtûL WlTo úTôuú\ Es[RôÏmUtßm CÕ ùRoúUô ©[ôv¥d ®û]p ûaTô≠Uo -«≠ÚkÕ ¡ûPdLl ùTß¡\Õ.Ød¡VUô] ùNVtûL WlToL[ôY]:

• ûShûWh ×hPô¥u WlTo

• ×ëûPp WlTo

• ûaTXôu WlTo

• ¨úVôl¬u WlTo

• £≠dLôu WlTo

Y. ùTVo RuûULs ETúVôLeLsGi

1 ûShûWh SpX ®¬§\u, úRnUô]jûR BhúPôùUôûTp PV¬às×hPô¥u WlTo G§odÏm RuûU, Ïû\kR Es[ ¥ë×Ls

ùYlT¨ûX«p Yû[kÕùLôÓjRp, ¿iP BÙs,Bd£úPNu, Ïû\kR CÝY≠ûU, ûadúWôv úLôl©£h¥.


68

Y. ùTVo RuûULs ETúVôLeLsGi

2 ×ëûPp ùThúWô≠Vm GiûQ úLv ãPô] Utßm Ï°of£Vô]Utßm BpLaôp LûWN≠]ôp ¨ûX«p úPl×L[ôL ¬lúToTô§dLlTÓm. CÕ ùYlTm Utßm ùNnÙm ùTôÝÕ TVuTÓjRlBd£úPN]ôp Tô§dLlTPôÕ TÓ¡\Õ. Utßm JúNô²tÏ A§LTô§lûTRWôÕ.

3 ûaTXôu ã¬V J° Utßm 150°C YûW Es[ ªu JVoLs Utßm úL©sLÞdÏWlTo ùYlT ̈ ûX«]ôp Tô§lTûPVôÕ úUp LYNUôL TVuTÓjRl

TÓ¡\Õ.

4 ¨úVôl¬u ¿iP BÙs, Bd£úPNu Utßm JVoLÞdÏ CuÑúXNu BLÜm,WlTo YôÙ®]ôp Tô§dLlTPôRÕ, SpX úL©sLÞdÏ Lôl× Eû\VôLÜm

ùYlTd LPjRûX RôeLd á¥VÕ, (LYNUôLÜm) TVuTÓjRlTÓ¡\ÕUtßm ùSÚlûT RôeLd á¥VÕ,Ïû\kR CVk§W®Vp RuûULsEûPVÕ.

5 £≠dLôu EVokR ùYlT¨ûX«p ùNVpTÓRp TYoúL©ÞdÏ CuÑúXN]ôLÜm(200°C), Yû[kÕ ùLôÓdÏm RuûU, Utßm FÕ EûX úLôd KY²uDWjRuûU Utßm A¬Uô]j§tÏ LhÓlTôhÓ JV¬Ûm, G@ÏG§Wô] RuûU, Bd³úPNàdÏ BûXLs Utßm AÔªu ¨ûX-G§Wô] RuûU, KúNôu, Bod¡e VeL°Ûm, ûa ©¬dÏYu£(arcing), SpX LPjRôjRuûU Utßm ù_]úWhPoL°Ûm, ùLô§LXu,ùYlTm LPjRôûU. CÕ JÚ £\kR ®Uô] ¨ûXV ®[dÏLs UtßmCuÑúXhPo BÏm. ¡úWuLÞdÏ TVuTÓjRlTÓ¡\Õ

UWj§u RuûULs Utßm TVuLs(Properties and uses of timber)

ùTôÕYô] RuûULs (General properties)

UWm ¸rLiP RuûULû[ ùLôi¥ÚdLúYiÓm.

• úSWô] SôoLs (A) CûZLs

• ©ú[²e ùNnÙm ùTôÝÕ ThÓlúTôußùUuûUVôL CÚdL úYiÓm.

• JúW Uô§¬Vô] YiQm.

• JÝeLô] YÚPYû[VeLs.

• Í®]v (Heaviness).

• LômTôdh UôÓX¬ L§oLs UtßmEß§VôL JÚe¡ûQkR SôojRuûU.

• C²ûUVô] UQm.

• ©ûQl× CpXôR, Ø¥fÑLs At\ RuûU.

• úUp TWl× T[T[lTôLÜm UtßmYô°]ôp ùYhÓm ùTôÝÕ ARu TtLs£dLôUp CÚdÏm YiQm CÚjRp.

YûLLs (Classification)

• UWeLs ¸rLiPYôß YûLlTÓjRlThÓs[].

a ùUuûUVô] UWm (Softwood)

b L¥]Uô] UWm (hardwood)

ùUuûUVô] UWm (Softwood timber)

• ùTôÕYôL F£ûVlúTôp ùU≠RôL Es[CûXLû[ EûPV UWeLs ùUuûUVô]UWm Gußm ALXUô] CûXLû[ EûPVUWeLs L¥]Uô] UWeLs G]ÜmA±VlTÓ¡u\].

• CkR UWm ùW£u Utßm PoTuûPuEs[RôL CÚdÏm.

• CkR UWm ùUuûUVô] UQm ÅÑmUWUôL CÚdÏm.

• SôoLs úSWôL CÚdÏm.

• AûUl× ùUuûUVôLÜm ùTôÕjRuûUùLôiPRôLÜm CÚdÏm.



69

• CÝjRûLûY G§olT§p Eß§VôLCÚdÏm.

• SôoLÞdÏ CûPúV TXÅ]UôL CÚdÏm.

• YÚP Yû[VeLs ®j§VôNUôL, ARôYÕJÚ TdLm ùUuûUVôL, ÖiÕû[LsUtßm ùY°¬V YiQjÕPuLôQlTÓm, B]ôp Utù\ôÚTdLmAPoj§VôLÜm Utßm AÝjRUô]YiQjÕPu CÚdÏm.

• ùTôÕYôL UWj§u YiQm ùY°¬Ùm(A) ûTu vlìv, @©o, Bx, ûLp,¥úVôPo Utßm TXYôL CÚdÏm.

L¥]Uô] UWj§u RuûULs (Properties ofhardwood)

• CqYûL ùTôÕYôL A§L NRÅRAªXjûRd ùLôi¥ÚdÏm.

• T°fùNu\ YiQj§p CÚdÏm.

• YÚP Yû[VeLs ®j§VôNUôL CÚdLôÕ.

• C§p úYûX ùNnYÕ L¥]UôL CÚdÏm.

• CÕ ùYhÓjRûLûY G§odÏm RuûUEûPVÕ.

• SôoLs Juû\Juß ©u²dùLôi¥ÚdÏm.

• CÕ ùTôÕYôL APoj§Vô]YiQeL[ô] ©WÜu, Kd, YôpSh, ¼d,UaôúLô², ºμm, Tô×p, Nôp UtßmTXYtû\d ùLôi¥ÚdÏm.

ETúVôLeLs (Uses)

ùUuûUVô] UWm (Soft timber)

• U≠Yô]j RuûU LôWQUôL U≠Ü YûLÅÓLÞdÏ LRÜLs, Nu]pLs, Aû\LXuLs RVô¬dLl TVuTÓ¡\Õ.

• G¬ùTôÚ[ôL ETúVôLl TÓjRlTÓ¡\Õ.

• £X UWeLs áûPLs Utßm ®¬l×LsRVô¬dL TVuTÓjRlTÓ¡\Õ.

• CRu ThûP £X CPeL°p BûPVôLTVuTÓjRlTÓ¡\Õ.

L¥]Uô] UWm (Hard timber)

• EVoRW Aû\LXuL[ô] SôtLô≠Ls,úUûNLs, úNôTôdLs, §YôuLs, TÓdûLAû\ Lh¥pLs Utßm TXYtû\RVô¬dLl TVuTÓjRlTÓ¡\Õ.

• EVoRW ÅÓLÞdÏj úRûYVô] Tô≠x,ùT«u¥e RuûUdÏ Ht\ YûL«pLRÜLs, Nu]p NhPeLs RVô¬dLTVuTÓjRlTÓ¡\Õ.

• LRô (katha) RVô¬dL TVuTÓjRlTÓ¡\Õ.

ªu CuÑúXhPWôL UWm (Wood as anelectrical insulator)

• CuÑúXhPWôL ETúVôLlTÓjRCmUWj§u FúP GiûQ (A )©\ùTôÚsLs Eh×Ïj§ TVuTÓjÕRp

ERôWQm.

• ªuNôW CVk§WeL°p ûYi¥e¡tÏCûPúV ûYdLlTÓm vXôh ùYh_v(slot wedges) BL TVuTÓjRlTÓ¡\Õ.

CuÑúXh¥e ùTôÚsLs (Insulatingmaterials)

®[dLm (Description)

CqYûL ùTôÚsLs ªuú]ôhPjûRØÝûUVôLúYô (A) A§LThNUôLúYôRÓdÏm RuûU EûPVÕ. (LPjRôjRuûU)CkR A§LThN RûPjRuûU ùTôÕYôL ùUdKm -p CÚdÏm 1 L]. ùNÁdÏ (1 ùUd Km =106 KmLs) BL CÚdÏm. ûP GXdh¬d(dielectric) Eß§ EûPVRôL CÚdÏm. CRu®[dLm Gu]ùY²p EVo ªu AÝjRmTVuTÓjRlTÓm ùTôÝÕ ùLôÓdLlThPR¥Uu Lôl× ùTôÚs EûPVúYô (A)TXÅ]m AûPVúYô ùNnVôÕ.

CuÑúXhP¬u RuûULs (Properties ofinsulators)

JÚ SpX CuÑúXhPo ùTôÚÞdÏúRûYVô]ûY CûY:

• ûa vùT£@©d ùW£vhuv (High specificresistance) ùUd Km/L] ùNÁ CÚdÏm. CÕªu CZlûTd ªLd Ïû\kR A[®tÏùLôiÓ YÚm.

• SpX ûPGXdh¬d Eß§jRuûU (Gooddielectric strength) ARôYÕ ©úWdPÜu ªuAÝjRj§u EVokR ThNm (¡úXôúYôph/ªÁ -p ùY°lTÓjÕm).

• SpX CVk§W®Vp Eß§jRuûU, CÝ¨ûX(A) AÝjR¨ûX (¨ßÜm úSWj§p UtßmúYûXf ãZ≠p HtTÓm) RûLûYjG§odÏm §\u).



70

• ùYlT¨ûX EVÚm ùTôÝÕ ̈ ûXûU ªLÏû\kR ¨ûX«p Tô§lTûPRp(CuÑúXh¥e RuûU EVoùYlT¨ûX«]ôp A§Lm Uô\ô§ÚjRp)ARôYÕ ªu NôR]eLû[ ØÝûUVôLCVdL ¨ûX«p ûYj§ÚdÏm ùTôÝÕTô§lTûPVô§ÚjRp BÏm.

• Y°UiPX DWlTRUô] ãr¨ûX«p DWmE±gNôR RuûU (Ïû\kR A[ÜDWjRuûU E±gNlThPôÛm,CuÑúXhP¬u RuûULs Ï±lTôLvùT£@©d ùW£vPuv (specific resistance)Utßm ûP GXdh¬d Eß§jRuûUÏ±l©hP A[Ü Ïû\kÕ ®Óm Yônl×A§Lm) úYiÓm.

CuÑúXhPoLs ªu Õû\«p TVuTôÓ

1 ûUdLô ûYi¥e¡p (vXôh CuÑúXN]ôL)

2 WlTo JVoL°p CuÑúXN]ôL

3 EXokR TÚj§ ûYi¥e

4 Yôo²x ûYi¥e

5 BvùTpPôv Cv§¬ùTh¥, ùLh¥pLs B¡VYt±u A¥lTôLj§p

6 ÏhPô TôofNô (Gutta ¿oêr¡ úL©sLsparcha)

7 ÀeLôu úUp¨ûX ªu Lm©LÞdÏ CûP«Xô] CuÑúXhPoLs

8 LiQô¥ -do-

9 EXokR UWm úUp ¨ûX ªu Lm©Lû[ RôeÏm ÏßdÏ

10 ©Vôv¥d Ñ®hÑL°u EPpTÏ§ (A) JVoL°u CuÑúXNu

11 GúTôû]h ªu Uôt±«u Tô©u

12 @ûTTo Tô©u RVô¬dL Utßm ûYi¥e CuÑúXhPWôL

13 GmTVo ¡[ôj ûYi¥e CuÑúXhPWôL

14 ùXRWônÓ úTlTo -do-

15 ªp≠úUdv úTlTo -do-

16 ©.®.£ JVo CuÑúXhPWôL

17 úTdûXh Ñ®hÑLs RVô¬dL Utßm CuÑúXhPWôL

18 ù`pXôd -do-

19 vúXh úT]p úTôoÓ RVô¬dL

20 TôW@©u ùUÝÏ AûPdL

RVô¬l×Ls Utßm CuÑúXhPoLs (Products and insulators)



71

¨û\, ¨û\«u AXÏLs, APoj§ Utßm GûP T«t£ 1.8.24

m - ùTôÚ°u ¨û\

g - ×®Dôól× ®ûNVôp HtTÓm ØÓdLmÁhPôó/®]ô¥2 = 9.81 m/sec2

V - ùTôÚ°u TÚU A[Ü

ρ - APôój§ (‘úWô’ G] EfNôõdLÜm')

W ApXÕ FG - GûP ApXÕ GûP ®ûN

¨û\ (Mass) (TPm 1)

JÚ ùTôÚ°p APe¡Ùs[TÚlùTôÚhL°u §¦Ü ¨û\ G]lTÓm¨û\«u AXÏ F.P.S Øû\«p TÜiÓ (lb)C.G.S. Øû\«p ¡Wôm (gr) M.K.S Utßm S.IØû\«p ¡úXô ¡Wôm £XNUVeL°p 1 PuGuTÕ 1000 ¡.¡WôUôL ETúVôLlTÓjRlTÓm.Kôó AX¡p CÚkÕ úYß JÚ AX¡tÏ Uôt\1000 LôW¦VôL TVuTÓ¡\Õ.UôtßmùTôÝÕ êu\ôYÕ RNU ×s°dÏUôt\Üm. ERôWQm 1 Pu = 1000 ¡úXô ¡Wôm1 ¡Wôm = 1000 ªp≠ ¡Wôm.

APôój§ (Density)

KWXÏl TÚUàs[ ùTôÚ°u GûP APôój§G]lTÓm. CRàûPV AXÏLs ¡Wôm/ùN.Á3

ApXÕ ¡.¡/ùP£.Á3 ApXÕ Pu/Á3.

APôój§ =

GûP (Weight) (TPm 2)

JÚ ùTôÚ°u ÁÕ ùNVtTÓm éª«u ûUVmúSôd¡V ×® Dôól× ®ûN GûP G]lTÓm.ùTôÚ°u ¨û\ Utßm ×®Dôól× ®ûNVôp

HtTÓm ØÓdLj§u ùTÚdÏ ùRôûL GûPG]lTÓm ùTôÚ°u GûP CPj§tÏ CPmUôßTôÓm.

GûP = W ApXÕ FG = ̈ û\ x ×®Dôól× ̈ ûXGi

= m x g

Øû\ ¨TkRû] YûWVß A[ÜAt\ AXÏ dLlThP Uôt\m

AXÏLs

©¬h¥v 1 TÜiPp 1 TÜih 32.2 TÜiPp Øû\ GûP (1lbx1ft/sec2

F.P.S. = 1TÜiPp)

ùNh¥ 1 ûPu 1¡Wôm 981 ûPuv ÁhPo GûP ¡Wôm 1gm x1cm/sec2

®]ô¥ Øû\ C.G.S. ÁhPo ¨ëhPu 1.¡.¡ GûP 1 ¨ëhPu = ¡úXô ¡Wôm ®]ô¥ = 1¡,¡x1Á/

®]ô¥2

Øû\ M.K.S. A¡X ¨ëhPu ¨ëhPu -do- EXL RW ̈ oQV Øû\ S.I.

1 ¡úXô GûP = 9.81 ¨ëhPu1 ¨ëhPu = 105 ûPuv( úRôWôVUôL 10¨ëhPu)

¨û\

TÚU A[Ü


72

¨û\ Utßm GûPdÏ CûPúVVô] ®j§VôNm, APoj§ UtßmAPoj§ GiÔdÏ CûPúVVô] ®j§VôNm T«t£ 1.8.25

¨û\ Utßm GûPdÏ CûPúVVô]®j§VôNm (Difference between mass and weight)

Y. ¨û\ GûPGi

1 TÚlùTôÚ°u ×® Dol× ®ûNVôp§¦Ü APe¡ DodLlTÓ¡\ÕEs[Õ

2 GkR CPj§Ûm CPj§tÏ HtT¨û\ Uô\ôÕ UôßTÓm

3 ùTôÚ°u ̈ û\ ×®Dol× ®ûNé_ó_÷VUôL CpûXùV²pCÚdLôÕ. GûP é_ó_õVUôL

CÚdÏm

4 CVp©Vp ®p RWôûNdRWôûNd ùLôiÓ GûPûVdùLôiÓ LQd¡PXôm¨û\ûVdLQd¡PXôm

5 vúLXôo ùYdPôoÏYôi¥h¥ ÏYôi¥h¥

6 ¿¬p êrL ¿¬p êrLûYlTRu êXm ûYlTTRu êXm¨û\ Uô\ôÕ ùTôÚ°u GûP

UôßTÓm

7 CRu AXÏ CRu AXÏ¡Wôm Utßm ¡úXô¡Wôm GûP¡úXô¡Wôm «p CÚdÏm,BÏm ®ûN«u AXÏ

¨û\ Utßm GûP ùYqúYßTôõUôQm ùLôiPÕ

ùTôÚ°u¨û\=TÚU A[Ü xAPôój§

GûP = ¨û\ x×®Dol× ®ûN«]ôp HtTÓmØÓdLm

GûP,APôój§ Utßm APôój§ Gi

TÚlùTôÚ°u §¦Ü GûPVôp UhÓmA[dLlTÓ¡\Õ. TÚU A[®u Ï±l×CpXôUp A[dLlTÓ¡\Õ. DVØmAÛª²VØm NU GûPVôL CÚkRôÛmDVj§u TÚU A[ûY Jl©ÓmùTôÝÕAÛª²Vj§u TÚU A[ûY ®P DVj§uTÚU A[Ü Ïû\YôL CÚdÏm.ClùTôÝÕSôm ùNôpXXôm. ARôYÕ AÛª²Vj§uAPôój§ûV ®P DVj§u APôój§ A§LmARôYÕ úYßYôô ójûR«p ùNôpXúYiÓUô]ôp AÛª²VjûRd Lôh¥ÛmDVj§u APôój§ A§Lm. (TPm 1 & 2)

¨û\dÏm TÚU A[ÜdÏm Es[ùRôPôó×Rôu APôój§ G]lTÓ¡\Õ.

TÚU A[®u ̈ û\ûVjRôu APôój§ GußùNôpXlTÓ¡\Õ. ERôWQm JÚ L] ùP£ÁhPôó Ri½ôõu ¨û\ JÚ ¡úXô ¡WômBÏm. ClT¥VôL APôój§Vô]Õ 1 ¡úXô /ùP..Á3 BÏm.

AXÏ

APoj§ ¸rLiPYôß A[dLlTÓ¡\Õ.

MKS/SI= Kg/m3, CGS - 1 gm/CC FPS–Lbs/Cft

§Pl ¡Wôm/ §WYe ¡Wôm/ùTôÚs L] ùN.Á Ls L ùN.Á

1 AÛª²Vm 2.7 Ri½o 1.00

2 DVm 11.34 ùThúWôp 0.71

3 Yôol× 6.8 to 7.8 Bd£_u 1.43CÚm×

4 G@Ï 7.75 to ¼Np 0.838.05 GiùQn

TÚlùTôÚ°u APôój§ Gi JlTPôój§Gußm AûZdLlTÓ¡\Õ.


73

ãj§Wm

APôój§ Gi ApXÕ JlTPôój§

APôój§ Gi =ùTôÚ°u ̈ û\

4°C p AúR TÚUàs[ ¿¬u¨û\

JÚ ùTôÚ°u APoj§ GuTÕ JWXÏT Ú U à s [A l ù T ô Ú ° u¨û\VôÏm.

CRu AXÏ ¡Wôm/ùN.Á 3, TÜih/L]A¥,Utßm ¡úXô/L.Á

JÚ ùTôÚ°u APoj§ Gi GuTÕ AlùTôÚ°u APoj§dÏm 40C ¿¬uAPoj§dÏm Es[®¡RUôÏm.CRtÏ AXÏLs¡ûPVôÕ, GiU§lTôp UhÓúUá\lTÓm.

JlTPoj§ =APoj§ =

¨û\

TÚU A[Ü ùTôÚ°u ¨û\

AúR TÚUàs[40C«p Es[ ¿¬u¨û\

úUtá±V AhPYûQ«p CÚkÕ, SômùLôÓdLlThP TÚU A[®u GûPûV (¼NpGiùQn) GkR AX¡Ûm TÚlùTôÚ°uAPôój§ Gi LôQXôm. AúR Uô§ôõ L]A[ûYÙm LiÓ©¥dLXôm.

APoj§dÏm Utßm APoj§ Gi(JlTPoj§ ) CûPúVVô] JlÀÓComparison Between Density And Specific Gravity(Relative Density)

APoj§ JlTPoj§ (A)APoj§ Gi

§PlùTôÚs APoj§ §WYm APoj§Gi Gi

1 AÛª²Vm 2.72 ùThúWôp 0.71

2 DVm 11.34 úThP¬ 1.2 toB£h 1.23

3 Yôol× 6.8 to Ri½o 1.00CÚm× 7.8

4 G@Ï 7.82 ¼Np 0.83GiùQn


JWXÏ TÚUàs[ ùTôÚ°u ¨û\

4°C «p Es[ JWXÏ TÚUàs[ ¿¬u¨û\

=


74

¨û\, GûP Utßm APoj§ B¡VYtßdLô] ùRôPo× LQdÏLÞm§\]ônÜ T«t£LÞm T«t£ 1.8.26

ERôWQm

• JÚ ùNqYL G@Ï RLh¥u A[ÜLs 220 x330 x 15 ª.Á CRu ¨û\ûV LQd¡Ó.(TPm 1) G@¡u APoj§ = 7.82 ¡Wôm/ùNÁ3

¨û\ = TÚU A[Ü x APoj§

= 22 x 33 x 1.5cm3 x 7.82 gm/cm3

= 1089 cm3 x 7.82 gm/cm3

¨û\ = 8.516 kg

Ri½¬u ̈ û\ = TÚU A[Ü x Ri½¬uAPoj§ = 250 ùP..Á3 x 1 ¡úXô / ùP . Á3

= 250 ¡úXô

GûP ®¬Ü = ̈ û\ x ×®Dol× ®ûN«]ôpHtTÓm ØÓdLm.

= 250 ¡ 10 Á/®]ô¥2

= 2500 ¡úXô.ÁhPo / ®]ô¥2

= 2500 ̈ ëhPu (1 ¡.¡ ÁhPo/®]ô¥2=1N)

3 15 ûPu ®ûNVô]Õ, ¨û\ `m' ÁÕùNÛjRlTÓ¡\Õ. CR]ôp 2.5 ùN.Á /®]ô¥2 -dÏ ØÓdLm HtTÓ¡\Õ. ̈ û\ûVLiÓ©¥.

1 ×ÜDol× GûP = 981 ûPu

15 ûPu = Gr.wt

®ûN = ̈ û\ x ®ûN«]ôp HtTÓm ØÓdLm

Gr.wt = ¨û\ x 2.5 ùN.Á/®]ô¥2

¡Wôm ùN.Á/®]ô¥2

= ¨û\ x 2.5 ùN.Á/®]ô¥2

¨û\ = ¡Wôm

= 0.00612 ¡Wôm

4 2 ¨ëhPu ®ûN 10 ¡úXô ¨û\«u ÁÕùNÛjRlTÓ¡\Õ ¨û\«u ÁÕùNÛjRlThP ®ûN«]ôp HtTÓmØÓdLjûR LiÓ ©¥.

®ûN = 2 ¨ëhPu ( 1 N = 1 ¡.¡/®]ô¥2)

®ûN = ¨û\ x ØÓdLm

2 ¡úXô ÁhPo / ®]ô¥2 = 10 ¡úXô xEtTj§Vô] ØÓdLm

2 x 1 ¡.¡ ÁhPo/®]ô¥2 = 10 kg xEtTj§Vô] ØÓdLm

EtTj§Vô] ØÓdLm= ÁhPo/®]ô¥2

= 0.2 ÁhPo/®]ô¥2

2 JÚ úNªl× Tôj§Wj§u Ri½oùLôs[Ü 250 ≠hPo ARàûPV GûPûV¨ëhP²p á\Üm. Ri½o Tôj§WmTWl©u ÁÕ ûYdLlThÓs[Õ (TPm 2)

(1 ≠hPo ¿¬u GûP = 1 ¡.¡Wôm ¿¬uGûP)

Ri½¬u APoj§ ¡Wôm / ùN.Á3 (ApXÕ)¡úXô / ùP . Á3

×®Dol× ®ûN«]ôp HtTÓmØÓdLm 10 Á/®]ô¥2 (úRôWôVUôL)

ùLôs A[Ü = 250 ≠hPo = 250 ùP . Á3

TÚU A[Ü


75

5 JÚ ¡úXô ¨û\ Es[ JÚ ùTôÚ°uGûPûV LQd¡ÓL. AR]ûPV ×®Dol×®ûN«]ôp HtTÓm ØÓdLm = 1 ¡úXô x9.81 ÁhPo/®]ô¥2

(1 ¡úXô ÁhPo / ®]ô¥2=/ ̈ ëhPu)

@ 9.81 ¡úXô ÁhPo / ®]ô¥2

= 9.81 ̈ ëhPu

Uô§¬ ¾o®p ‘g’ «u U§l× 10 ÁhPo/®]ô¥2 G] GÓjÕd ùLôs[lThÓs[Õ. Ï±l©hÓ GÕÜmá\®pûX Gu\ôp CqYôßGÓjÕd ùLôs[Xôm.

.• ùYtß úLô[j§u ùY°l×\ UtßmEh×\ ®hPeLs Øû\úV 150 Utßm 70ª.Á CRu ¨û\ûV LiÓ ©¥ClùTôÚ°u APoj§ 7.5 ¡Wôm/ùN.Á3

(TPm 3)

6 JÚ Lô¬u ¨û\ 800 ¡úXô. ARàûPV®ûN GûPûV LiÓ©¥ (9.81 Á/®]ô¥2

G] GÓjÕd ùLôs[Üm)

( 1 ¨ëhPu = 1 ¡¡.ª/ùNÁ2)

Lô¬u ®ûN GûP = Lô¬u ¨û\ x ×®Dol×®ûNVôp HtTÓm ØÓdLm

= 800 x 9.81 ¨ëhPu

= 7848 ̈ ëhPu

7 JÚ EÚû[ Y¥Yô] ùRôh¥«u ®hPm2 ÁhPo ARu BZm 3.5 ÁhPo C§pùThúWôp ¨WlThÓs[Õ ùThúWô≠uGûPûV Pu²p LiÓ ©¥dLÜmùThúWô≠u APoj§ 720 ¡¡/Á3. (TPm 4)


= TÚU A[Ü x 7.5 ¡/ùNÁ3

D= 150 ªÁ = 15 ùNÁ R= 7.5 ùNÁ

d = 70 ªÁ = 7 ùNÁ r = 3.5 ùNÁ

úLô[j§u TÚU A[Ü =

=

=1587.5 cm3


= x 7.5

¨û\ = 1587.5 ùNÁ3 X 7.5 ¡Wôm/ùNÁ3

= 11906.6 ¡Wôm =11.9 ¡¡ = 12 ¡¡ (ùNôpXXôm)

ùRôh¥«u TÚUA[Ü

= 3.14 x 3.5 m3 = 10.99 m3

JÚ L]ÁhPo = 1000 ≠hPo

ùRôh¥«u TÚU A[Ü = 10.99 x 1000 ≠hPo

ùThúWô≠u APoj§ = 720 ¡/Á3

ùThúWô≠u GûP ¡úXô®p =

= 10.99 x 1000 ≠hPo x 720 ¡¡

= 720 x 10990 ¡¡

ùThúWô≠u GûP Pu²p (ùUh¬d AXÏ)

(Metric Units)

= 7912.8 Pu]v

8 úThP¬ B£h¥u APoj§ Gi 1.3 CÕEÚû[ Y¥YUô] ùRôh¥«p¨WlTlTÓ¡\Õ. CRu APoj§ûVLiÓ©¥.

Ri½¬u APoj§ = 1000 ¡/ùNÁ3

APoj§ Gi (A) JlTPoj§



76

ClùTôÝÕ úThP¬ B£h¥u APoj§

= APoj§ Gi x Ri½¬u APoj§

= 1.3 x 1000 ¡/ùNÁ3

= 1300 ¡/ùNÁ3

§iUlùTôÚ°u APoj§ GiûQLôÔRp

§iU ùTôÚhL°u APoj§ GiLû[ ̧ rLiPYôß LôQXôm.

1 Bod¡ª¼v RjÕYm (Archemedies principle)

2 ¿oU Uô²Ls (Hydrometer)

Bod¡ª¼v RjÕYm

JÚ ¿oUj§às JÚ ùTôÚs ØtßúUô (A)TÏ§úVô êr¡«ÚdÏm úTôÕ AR]ôp CPmùTVodLlThP ¿oUj§u GûP AlùTôÚs¿oUj§p CZkR GûPdÏf NUUôL CÚdÏm.

¿oUj§p ùTôÚ°u GûP =

= ùTôÚ°u ùUôjR GûP - ùTôÚ°]ôp ùY°úVt\lThP ¿¬u GûP

CRu A[Ü é_ó_õVUôL CÚl©u ùTôÚs¿¬p ªRdÏm. CÕ JÚ G§o ®û]VôÏm JÚùTôÚs êr¡ CÚkRôp ARtÏ Ht\ôt úTôp¿Úm ùY°úV± CÚdÏm. AkR ¿oAlùTôÚ°u GûPVôÏm. ùTôÚs ¿¬pêr¡]ôp., AÕ úSo ®û]VôÏm.

¿¬p AªZdá¥VÕm, LûWVdá¥VÕUô]§iUj§u APoj§ Gi

§PlùTôÚû[ úRôóÜ ùNnÙmùTôÝÕ, Ri½ôó Utßm ¿ôóUj§pLûWVôR ùTôÚ[ôL CÚdL úYiÓm.CqYôß úRô óÜ ùNnVlThP§PlùTôÚ°u APôój§ GiLôQXôm.

ERôWQm

1 Lôt±p G@Ï Õi¥u GûP 160kgf UtßmØÝûUVôL Ri½ôõu êr¡CÚdÏmùTôÝÕ ARu GûP 133kgf. AkRG@Ï Õi¥u TÚU A[Ü Utßm APôój§Gi LôiL.

Lôt±p §PlùTôÚ°u GûP= 160 kgf

Ri½ôõp §Pl ùTôÚ°u GûP = 133 kgf

Ri½ôõp CZdÏm GûP = 27 kgf

Bôód¡ª¼v RjÕYj§u T¥ §PlùTôÚsRi½ôõp CZdÏm GûP = ùY°úVt \lTÓmRi½ôõu L] A[Ü

ùY°úV±V Ri½ôõp L] A[Ü= 27 cm3

§PlùTôÚ°u L] A[Ü = 27 cm3

ùTôÚ°u ̈ û\

AúR TÚUàs[ 40C p Es[ ¿¬u ̈ û\

Lôt±p ùTôÚ°u GûP

¿oUj§p CZdÏm GûP=

¿¬p AªZd á¥VÕm, LûWVd á¥VÕUô]§iUj§u APoj§ Gi

Lôt±p ùTôÚ°u GûP x ¿oUj§uAPoj§ Gi

¿¬p CZdÏm GûP=

¿ôóUj§u APôój§ Gi

§iUm ¿¬p CZdÏm GûP

AúR ùTôÚs ¿oUj§p CZdÏm GûP=

G@¡u ̈ û\Õi¥u L] A[Ü

G@Ïj Õi¥uAPoj§ =

= = 5.93

G@¡u APoj§Ri½¬u APoj§

APoj§ Gi =

G@Ï Õi¥u APoj§ Gi = 5.93

2 Lôt±p JÚ EúXôLj Õi¥u GûP 6.5 kgfUtßm Ri½ôõp 3.5 kgf AÕ ØÝûUVô]¿ôõu êr¡ CÚd¡u\Õ. ARàûPVGûPûV LôiL. ARàûPV ¿ôóUj§uAPôój§ Gi 0.8.

Lôt±p EúXôLjÕi¥u GûP= 6.5 kgf

Ri½ôõp EúXôLj Õi¥u GûP= 3.5 kgf

¿ôõp CZdÏm GûP = 3.00 kgf (6.5 - 3.5)

EúXôLj§u APôój§ Gi

Lôt±p EúXôLj§u GûP

Ri½¬p EúXôLj§u GûP=



77

Bôód¡Á¼v RjÕYjûR TVuTÓj§úUtá±V Ø¥Ü A±VlTÓ¡\Õ.

¿ôóU Uô²Lû[ TVuTÓj§ ¿ôóUj§uAPôój§ GiLû[ LôQXôm. C§pùTôÕYô] ¿oU Uô² ¨dLpNu ¿oUUô²BÏm. CÕ ®j§VôNlTÓm GûP Es[B]ôp ¨ûXVô] êrÏm YûL BÏm.

¿ôóUj§u APôój§ Gi =

¿ôóU Uô²«u GûP+êrÏYRtÏ úRûYVô]GûP

¿oU Uô²«u GûP + ¿oU Uô²ûVêrL¥dLj úRûYVô] GûP (¿¬p AúRA[Ü Ï±ÂÓ YûW êr¡Ùs[ EVWm)

¿oU Uô²«u ¿oUjûR Ï±dÏm ̈ ûXVô]Ï±ÂÓ

úUtÏ±l©hÓs[ A[Ü YûW«p Ri½o

¿ôóUj§p EúXôLjÕi¥u GûP= W G]dùLôsL

∴

¿ôóóUj§p EúXôLm CZdÏm GûP = 6.5kgf_W

w = 6.5 kgf - 3 kgf X 0.8 = 4.1 kgf

¿ôóUj§p EúXôLm CZkR GûP = 4.1 kgf.

3 Lôt±p §P ùUÝ¡u GûP 21 kgf. GûP 19kgf EúXôLj ÕiûPÙm ùUÝûLÙmCûQjÕ Ri½ôõp êrLûYjRôpARàûPV GûP 17 kgf BÏm. ùUÝ¡uAPôój§ Gi LiÓ©¥dLÜm.

Lôt±p ùUÝ¡u GûP = 21 kgf

EúXôLm + ùUÝ¡u, Ri½ôõp GûP= 17kgf

Lôt±p EúXôL Õi¥u GûP= 19 kgf

Ri½ôõp ùUÝ¡u GûP = 17 kgf -19 kgf

= - 2 kgf

¿¬p ùUÝ¡u GûP CZl×

= 21 kgf - (-2kgf)

= 23 kgf

Y. EúXôLm APôój§Gi ¡Wôm/L.ùNÁ

1 AÛª²Vm 2.7

2 Yôôól©Úm× 6.8 - 7.8

3 ùNm× 8.92

4 ReLm 19.32

5 CÚm× 7.86

6 DVm 11.34

7 ¨dLp 8.912

8 ùYs° 10.5

9 G@Ï 7.75 - 8.05

10 ùYsÇVm 7.31

11 ÕjRSôLm 7.14

12 ûYWm 3.51

13 ©vUj 9.78

14 ©jRû[ 8.47

15 TôvTWv ùYiLXm 8.7 - 8.9

16 Iv 0.93

17 Lôtß 0.0013

18 TôRWNm 13.56

19 ùThúWôp 0.71

20 ¼Np 0.83

21 UiùQiùQn 0.78 - 0.81

22 Ri½ôó 1.0


=

¿oUj§u APoj§ Gi =¿oUj§p CZkR GûP

Ri½¬p CZkR GûP

ùUÝ¡u APoj§ Gi


78


1 ¿[m(l) = 1800 ª.Á

ALXm(b) = 65 ª.Á

EVWm(h) = 12 ª.Á

APoj§ (ρ) = 7.85¡/ùNÁ3

(m) = ________¡¡

2 ù L ô s [ Ü = 3 6≠hPo®hPm(d) = 32 ùNÁ

EVWm(H) = ___ùNÁ

3 ùY°®hPm(D) =74 ª.ÁEs®hPm(d) = 68ª.Á¿[m(l) = 115 ª.ÁAPoj§ (ρ)= 8.6 ¡/ùNÁ3

(m) = ________¡¡

4 ®hPm1(D 1 )= 80

ª.Á®hPm

2(D2)=61 ª.Á

Es®hPm(d) = 39ª.Á¿[m(L) = 112 ª.Á¿[m(l) = 90 ª.ÁAPoj§(ρ) = 7.85¡/ùNÁ3

(m) = ________¡¡

5 ®hPm(D) = 44 ª.Á®hPm(d) = 20 ª.Á¿[m(L) = 120 ª.Á¿[m(l 1) = 60 ª.Á¿[m(l 2) = 40 ª.ÁAPoj§(ρ) = 7.85¡/ùNÁ3

(m) = ________¡¡

6 ¿[m(L) = 120 ª.ÁALXm(B) = 90 ª.ÁALXm(b 1)= 60 ª.ÁALXm(b 2)= 30 ª.Á®hPm(d) = 55 ª.ÁEVWm(H) = 42 ª.ÁEVWm(h) = 18 ª.ÁAPoj§(ρ) = 7.85¡/ùNÁ3

(m) = ________¡¡

7 ¿[m(L) = 200 ª.Á¿[m

1(l 1) = 75 ª.Á

¿[m2(l 2)= 50 ª.Á

ALXm(B) = 80 ª.ÁEVWm(H) = 110 ª.ÁEVWm(h) = 45 ª.ÁAPoj§(ρ) = 2.7 ¡/ùNÁ3

(m) = ________¡¡

8 L] A[Ü(V) = 320L.ùN.ÁAPoj§(ρ) = 8.9 ¡/ùNÁ×®Dol× (g) =9.80665 ÁhPo/®]ô¥2

(m) = ________¡¡(FG)=______¨ëhPu

9 ùLôs[[Ü = 35≠hPo×®Dol×(¡) = 10ÁhPo/®]ô¥2

FG = ___ ¨ëhPu

10 ùN«²u ̈ û\(m 1 )= 150 ¡úXô

ùUôjRm FG = 8¡.¨ëhPuTÞ = ______¨ëhPu¨û\ (m2)= __¡úXô

11 GûP(W) (FG) = 22.5¨ëhPu

L] A[Ü (volume) =______

12 ®ûN(F) = 250 d N

L] NÕWj§uTdLm = ______ ª.Á

(L] NÕWj§uùY«h úTXuv`F')



79

13 Au TôXuÑÓúXôh ùNh Al=16 cNú T X u £ eGûP«u ®hPm ø= 20 ª.Áú T X u £ eGûP«u A[Ü (l)=______ ª.Á

14 ®hPm(d 1)= 40 ª.Á

¨û\(m 1)= 9 x 10 –2

¡¡

BWm 1 = BWm 2

®hPm(d 2)= 60 ª.Á

FG 2 = ______¨ëhPu

15 ¿[m(l) x ALXm(b)= 1 Á2

FG = 7.85 x 10–2

¡.¨ëhPuL]m(s) = ______ ª.Á

16 ®ûN (F) = 400¨ëhPu

(m) = ________¡¡

17 ¨û\1(m 1)= 200

¡Wôm

FG = 16 ¨ëhPu

®ûN(F) = ______ dN

18 R = 14 ¡. ¨ëhPu

(m) = ________¡¡

19 L] A[Ü(V) = 4ùP.Á3

FG = 10.8 daN

APoj§(ρ) =______¡/ùNÁ3

20 ¿[m(l) = 500 ª.ÁALXm(b) = 300 ª.ÁEVWm(H) = 250 ª.ÁG i ù Q n « uAPoj§(ρ) = 0.9¡/L.ùNÁ3

¨û\(m) = 2.5 kgEVWm(h) = ____ª.Á

21 G g £ u á ≠ eúPhPô ùLôÓdLlT h Ó s [ Õ .ú R ¥ ú V h P ¬ pRi½o = 10≠hPoLiÓ©¥Ri½¬u ¨û\ =__________ ¡¡(JÚ ≠hPo = ùP£ÁhPo3 L]A[Ü)Ri½¬u APoj§= 1 ¡¡/ùP..Á3

22 EÚû[«u ¿hPpA[ÜLsùLôÓdLlThPúPhPôù Y ° l × \®hPm(OD) = 111ª.Á

Eh×\ ®hPm(ID) = 103 ª.Á¿[m = 240 ª.ÁùTôÚs = C.I = Yôol× CÚm×Yôol©Úm©u APoj§ (C.I) = 7.259 ¡/ùNÁ3

CRàûPV ¨û\ûVd LiÓ©¥ _________ ¡¡

23 LhCVôu ©u(§PUô]Õ)ùLôÓdLlThPúPhPô®hPm = 200 ª.Á¿[m = 70 ª.ÁùTôÚs = (M.S)ªÚÕ G@ÏAPoj§ = 7.85 ¡/ùNÁ3

CRàûPV¨û\ûVLiÓ©¥dLXôm¨û\ ________ ¡



80

24 A Û ª ² V m©vPuù L ô Ó d L l T hÓs[Õ úPhPô®hPm = 80 ª.Á¿[m = 100 ª.ÁA Û ª ² V j § uAPoj§ = 2.7 ¡/ùNÁ3

CRàûPV ¨û\_______ ¡¡

25 EsÇPt\ EÚû[(Lôvh ©Wôv)ùLôÓdLlThPúPhPôùY°l×\®hPm(O.D) = 150 ª.ÁEh×\®hPm(I.D) =120 ª.Á

©jRû[«u APoj§ = 6.89 ¡Wôm/L] ùNÁ

ãj§WjûR TVuTÓjRp = ( (R3)3)

LiÓ©¥dLÜmEsÇPt\ EÚû[«u ¨û\ = _______ ¡¡

26 ¼Np ùRôh¥

ùLôÓdLlThPúPhPô

®hPm = 400 ª.Á

¨Wl×m BZm (h)= 600 ª.Á

vTôu_õ B@l B«p = 0.8

Ri½¬u APoj§ = 1000 ¡¡/Á3

LiÓ©¥

ùRôh¥«p Es[ B«≠u ¨û\ = ______ ¡¡

27 YûWVßdLÜm

¸rLiP ùNôtLû[ YûWVßdLÜm

a ¨û\

b GûP

c APoj§

d APoj§ Gi

28 Yi¥«u GûPûV Uôt\m ùNnVÜm

×®Dol× (g) = 10 Á/®]ô¥2

®ûN GûP ¨û\

a 480 ¨ëhPu _______

b 14800 ̈ ëhPu _______

c 2000 ¨ëhPu _______

d 7000 ¨ëhPu _______

29 Yi¥«u ¨û\ AXûL Uôt± GÝRÜm

×®Dol× (g) = 9.81 ÁhPo/®]ô¥2

Yi¥«u ¨û\ ARu GûP«p

a 1200 ¡¡ ________ ̈ ëhPu

b 800 ¡¡ ________ ̈ ëhPu

c 700 ¡¡ ________ ̈ ëhPu

d 900 ¡¡ ________ ̈ ëhPu

30 úLô¥hP CPeLû[ éoj§ ùNn

EúXôLjûRÙm §WYjûRÙm Jl©PÜm

ùTôÚhLs APoj§ APoj§ Gi

a DVm 11.34 _______

b ùNm× 8.92 _______

c Yôol× CÚm× 7.20 _______

d ùThúWôp 0.71 _______

e ¼Np 0.83 _______

f Npé¬d B£h 1.84 _______

31 a Utßm b «p úLô¥hP CPeLû[ N¬Vô]YôojûRL[ôp ¨WlTÜm.

a Ri½¬u APoj§ = 1000 ¡¡/ÁhPo3.

ûSh¥¬d B£h¥u APoj§ Gi 1.2Gu\ôp ûSh¥¬d B£h¥u APoj§ =_______

b ùTôÚhLs APoj§ APoj§ Gi

i Ri½o 1000 ¡¡/Á3 _______

ii AÛª²Vm 2.7 ¡/ùNÁ3 _______

iii CÚm× 8 ¡/ùNÁ3 _______

iv ùNm× 8.7 ¡/ùNÁ3 _______

c ùTôÚ°u ¨û\ = L]A[Ü x _______

d ®ûN«u GûP = ¨û\ x _______

e CRu ÑÚdLeLû[ GÝÕL

i ùULô¨ëhPu_______

ii ¡úXô¨ëhPu To vùLôVo ÁhPo_______

f JÚ ≠hPo Ri½o _______¡¡.



81

KnÜ, CVdLm, úYLm, §ûN úYLm, úYLm Utßm §ûNúYLj§tLô]úYßTôÓ, ØÓdLm Utßm Ïû\ØÓdLm T«t£ 1.9.27

ùTôÚ°u KnÜ ¨ûX (Body at rest)

JÚ ùTôÚs Ñtß×\ ãr¨ûXdÏ HtT Ru¨ûX«p CÚkÕ Uô\ôUp CÚlTÕ KnÜ¨ûX G]lTÓm.

ùTôÚ°u CVdLm (Body at motion)

JÚ ùTôÚs Ko CPj§≠ÚkÕ úYßJÚCPj§tÏ Ru ̈ ûXûV Uôt±d ùLôsYRtÏARôYÕ CP Uôt\m AûPYRtÏ CVdLmGuß ùTVo. JÚ ùTôÚs CVeÏmúTôÕúSodúLôh¥p CPm ùTVokÕ ùNpÛUô«uAq®VdLm úSodúLôhÓ CVdLm G]lTÓm.JÚ ùTôÚs CVeÏm TôûR Yû[YôLAûUÙUô]ôp Aq®VdLm YhP Nôôó×CVdLm G]lTÓm.

CVdLm NmTkRlThP ùNôtLs (Termsrelating to motion)

CPlT«t£ (Displacement)

ùTôÚ°u ùRôPdL ¨ûXdÏm, Cß§¨ûXdÏm CûPúV úSôódúLôh¥p Es[çWm AlùTôÚ°u CPlùTVof£G]lTÓm.

úYLm (Speed)

JÚ CVeÏm ùTôÚs JÚ Ï±l©hP úSWj§pSLÚm çWm úYLm G]lTÓm. CRtÏ A[ÜUhÓúU EiÓ. §ûN¡ûPVôÕ. G]úY CÕvúLXôo A[YôÏm.

úYLm= JÚ Ï±l©hP AXÏ úSWj§p SLÚmçWm.

AXÏ = ÁhPo/ùNLih, ¡úXôÁhPo/aYo(U¦)

§ûN úYLm (Velocity)JÚ CVeÏm ùTôÚs JÚ Ï±l©hP úSWj§pÏ±l©hP §ûN«p ùTßm CPlùTVof£úVAlùTôÚ°u §ûN úYLm G]lTÓm. CûRÏ±l©ÓmùTôÝÕ Gi U§lûTÙm§ûNûVÙm úSodúLôh¥p Ï±l©PúYiÓm. G]úY CÕ ùYdPôôó A[YôÏm.§ûN úYLm úSodúLôh¥úXô ApXÕúLôQ §ûN«úXô CÚdLXôm úSodúLôh¥p CVeÏm §ûN úYLj§u AXÏÁhPo/ùNLih,

¡úXôÁhPo/U¦, ûUp/U¦

úYLm Utßm §ûN úYLj§u úYßTôÓLs

úYLm §ûNúYLm

úYLm GuTÕ JÚ §ûNúYLm GuTÕ JÚùTôÚs JÚ ùTôÚs JÚ Ï±l©hP®]ô¥ úSWj§p §ûN«p JÚ ®]ô¥SLÚm çWm BÏm úSWj§p ùTßm CPl

ùTVof£ BÏm.

úYLj§p §ûN §ûN úYLj§p ARuÏ±l©ÓYÕ Gi U§l×, §ûN B¡VCpûX úYLm CWiÓm Ï±dLlTÓmARu Gi U§l©p UhÓúUÏ±dLlTÓm

úYLm = §ûNúYLm =(LPkR çWm)

GÓjÕdùLôiPçWm

=Ï±l©hP §ûN«p

CPlùTVof£

GÓjÕdùLôiPúSWm

=

ØÓdLm (Acceleration)

JÚ ùTôÚ°u §ûN úYLm UôßmúTôÕAlùTôÚs ØÓdLm ùTß¡\Õ. JÚùTôÚ°u ØÓdLm GuTÕ JÚ Ï±l©hPúSWj§p §ûN úYLj§p HtTÓmUôßTôPôÏm. CRu AXÏ ÁhPo/ùNLih2.CÕ JÚ ùYdPôôó A[YôÏm.

ØÓdLm (a) =

AXÏ = ÁhPo/ùNLih2

u = BWmT §ûNúYLm (Á/ùNLih)

v = Cß§ §ûNúYLm (Á/ùNLih)

s = CûPlùTVof£ (ÁhP¬p)

t = LôXm (A) úSWm (®]ô¥)

a = ØÓdLm (Á/ùNLih2 (úSoUû\«p)

R = G§oØÓdLm (A) úYLjR[of£ (Á/ùNLih2 (G§oUû\«p)

CVdL NUuTôÓLs (Equations of motion)©\Ï v = u + at

ùTôÚ°u Cß§ §ûN úYLm =BWmT§ûNúYLm + ØÓdLm x LôXm

s = ut + at2 Utßm v2 – u2 = 2as

v2 = u2 + 2as

LPkR çWm

GÓjÕdùLôiPçWm=

§ûNúYLj§p HtTÓm UôßRp

LôXmÁ/ùN2


82

G§o ØÓdLm (A) úYLjR[of£ (Retardation)

JÚ ùTôÚ°u Cß§ §ûN úYLjûRLôh¥Ûm BWmT §ûN úYLm Ïû\YôLCÚkRôp. ARtÏ ØÓdLm Guß ùTVo. JÚùTôÚ°u BWmT §ûN úYLjûR Lôh¥ÛmCß§ §ûN úYLm Ïû\YôL CÚkRôp ARtÏG§oØÓdLm G]l ùTVo. êuß CVdLNUuTôÓLs Es[].

v = u – at

Cß§ §ûN úYLm=BWmT§ûNúYLmþØÓdLm x úSWm

s = ut – at2

CPlùTVof£ = BWmT§ûN úYLmxúSWmþØÓdLmxúSWm2

u2–v2 = 2as

BWmT§ûN úYLm2þCß§ §ûN úYLm2 = 2 xØÓdLm x CPlùTVof£

NWôN¬ úYLm (Average speed)

Vm - NWôN¬ úYLm ÁhPo/¨ªPm, (ÁhPo/ùNLih)

n - YhP CVdLm JÚ ¨ªPj§tÏ ApXÕJÚ ¨ªPj§p GjRû] vhúWôd

s - CPlùTVof£, vhúWôd¡u ¿[m

ÅfÑ úYLm (Stroke speed) (TPm 1)

¡Wôe©u kþ×s°«p JÚ Ñtß Ñt±]ôp,AkR çWj§tÏ TYoNô ©ú[h SLÚm çWm= 2 x s

BûLVôp JÚ ¨ªPj§tÏ ‘n’ Ñtß çWmÑt±]ôp ARu çWm = 2 x s x n. ©ú[¥uÅfÑ ÁhP¬p ùLôÓdLlTÓYR]ôp NWôN¬úYLjûR LôQ

Vm = 2 x s x n

©vPu úYLm (Piston speed) (TPm 2)

©vPu Øuàm ©uàm SLÚm úUpTÏ§Utßm ¸r TÏ§«p Es[ ùPhùNuP¬pARu úYLm JúW ºWôL Uô± ùLôiúPCÚdÏm. CkR úL£ÛmáP NWôN¬ úYLm

Vm = 2 x s x n -I ªp≠ ÁhP¬Ûm Utßm n IJÚ ¨ªPj§tÏ GjRû] ÑtßdLs GußmUtßm Vm I ÁhPo /ùNLih¥pá\lThÓs[Rôp.

Vm = 2 x s x ÁhPo/¨ªPm

=

S I ÁhP¬p ùLôÓjRôp ©\Ï

Vm = 2 x s x = s x ÁhPo/ùNLih

2 x s CWiÓ ÅfûN Ï±dÏm.¬£l×úWôd`u CVdLj§p, NWôN¬úYLjûR LQd¡p GÓjÕdùLôs[úYiÓmVm = 2 x s x n ÁhPo/¨ªPm C§p s IÁhP¬p ùLôÓdLlThÓ CÚkRôp.

ERôWQm (Example) (TPm 3)

GdvhÚNu ©Wv£p Es[ ¡Wôe¡u BWm20 ùN.Á Utßm ARu úYLm 30 rpm NWôNôõúYLjûR ÁhPo /¨ªPm, ÁhPo/ùNLih¥pLQd¸Ó ùNnVÜm.

s = ®hPm = 40 ùNÁ

¡Wôe JÚ Øû\ Ñt±]ôp ©vPu SLÚmÕWWm 2s = 80 ùNÁ

Vm = 2 x 400 x ÁhPo/¨ªPm

= 24 ÁhPo/¨ªPm = 0.4 ÁhPo/ùNLih



83

¨ëhP²u CVdL ®§Ls (Newton laws ofmotion)

×®Dol× ®ûNVôp HtTÓm CVdLj§uNUuTôÓ (Equations of motions under gravity)

úUp úSôd¡ ¸r úSôd¡

V = u – gt v = u + gt

s = ut – gt2 s = ut + gt2

u2–v2 = 2as V2–u2 = 2as

×®Dol× ®ûNVôp HtTÓm CVdLm (Motionunder gravity)

JÚ ùTôÚs ¨ûX«p CÚkÕ ¸r úSôd¡®ÝmúTôÕ ARàûPV §ûN úYLmA§L¬dÏm Utßm RûWûV ùRôÓmùTôÝÕARu §ûN úYLm A§L ThNUôL CÚdÏm.BûLVôp ×®Dol× ®ûNVôp JÚ ùTôÚs¸rúSôd¡ YÚmùTôÝÕ ºWô] ØÓdLmHtTÓ¡\Õ. CkR CVdLm úUpúSôd¡CVeÏmùTôÝÕ, AkR ùTôÚÞdÏG§oØÓdLm HtTÓ¡\Õ CkR ØÓdLm×®DolTôp HtTÓ¡\Õ. CÕ ‘g’ GußÏ±dLlTÓ¡\Õ.

EkRm (Momentum)

JÚ CVeÏm ùTôÚs Utù\ôÚ ùTôÚÞPuúUôÕmúTôÕ, A§p AûNûY EiPôdÏm§\ûU EkRm G]lTÓm. CÕ ¨û\ûVÙm§ûN úYLjûRÙm ùTÚd¡ YÚm ùRôûLdÏNUm BÏm. EkRj§u AXÏ ¡úXô ÁhPo/ùNLih.

EkRm = ùTôÚ°u ¨û\ x §ûN úYLm

¨ëhP²u CVdL ®§Ls (Newton’s laws)

ØRp ®§ (First law)

RuÁÕ ùY°®ûN HÕm RôdLôRYûWJqùYôÚ ùTôÚÞm R]Õ AûNVô¨ûX«úXô ApXÕ ºWô] §ûN úYL¨ûX«úXô ùRôPokÕ CÚdÏm.

CWiPôm ®§ (Second law)

JÚ ùTôÚ°u EkRm Uôßm ÅRm ARuúUp ùNVpTÓm ®ûNdÏ úSo®¡Rj§pAûUYúRôÓ Aq®ûN«u §ûN«úXúVCÚdÏm.

êu\ôm ®§ (Third law)

JqùYôÚ ®ûNdÏm ARtÏ NUUô]G§o®ûN Juß EiÓ.

¬®h CûQl©p v¥Wôl ÁÕ NUUô] ®ûNùNVpTÓ¡\Õ Utßm AÕ G§o §ûN«ÛmùNVpTÓ¡\Õ. F2. (TPm 4)

EkR A¯®uûU ®§ (Law of conservation ofmomentum)

JußdÏ úUtThP ùTôÚsLsúUô§dùLôsÞmúTôÕ úUôRÛdÏ ØuEs[ ùUôjR EkRlTôÓ úUôRÛdÏl©uEs[ ùUôjR EkRlTôh¥tÏfNUm ApXÕúUôRÛdÏ ©\Ï HtTÓm EkRm éw´VmBÏm.

m1 - JÚ ùTôÚ°u ¨û\

v1 - SLÚmùTôÝÕ HtTÓm §ûN úYLm

m2 - CWiPôYÕ ùTôÚ°u ̈ û\

v2 - SLÚmùTôÝÕ HtTÓm §ûN úYLm

EkRm = ¨û\ x §ûNúYLm = ùTôÚ°u ¨û\x ARu §ûNúYLm

EkR®¡R Uôt\m = ùTôÚ°u ÁÕ HtTÓm®ûN

( )F

t

uVm =

−⎟⎠⎞

⎜⎝⎛

®ûN = ¨û\ x ØÓdLm

CmTôdhÓdÏ Øu]ôp CWiÓ ùTôÚ°uEkRm = CmTôdhÓdÏ ©\Ï HtTÓm EkRm.

m1 x v1 + m2 x v2 = (m1 + m2)V

LûX ùNôtLs - YôL]eL°p Es[ £XERôWQeLs (Terms - Some Examples in vehicles)

CPlùTVof£ (Displacement)

©vP²u CPlùTVof£ GuTÕ CWiÓùPh ùNuPÚdÏ CûPúV Es[CûPùY° (TDC Utßm BDC) £≠iP¬p©vPu SLÚm çWm. (TPm 5)

úYLm (Speed)

CûR CWiÓ YûL«p Ï±l©PlTÓ¡u\Õ.

– YôL]j§u úYLm - in kmh/mph



84

– CVk§Wj§u úYLm - in rpm

§ûN úYLm (Velocity)

JÚ úUôhPôó YôL]m, ùTôÕYôL TôûR«pùNpÛm ùTôÝÕ ARàûPV úYLm Utßm§ûN«p UôßRp HtTÓm. AR]ôp CûRdùLôiÓ YôL]j§u §ûN úYLmLQd¡PlTÓ¡\Õ.

ØÓdLm (Acceleration) (TPm 6)

TôûR«p YôLj§u úYLm A§L¬dÏmùTôÝÕ CÕ ØÓdLm G]lTÓ¡\Õ.

Ïû\ØÓdLm (A) G§o ØÓdLm (CÕ úUÛm® [ d L l T h Ó s [ Õ ) Y ô L ] mùNpÛmùTôÝÕ, ©úWd úTôhPôp,YôL]j§u úYLm Ïû\¡u\Õ. CÕÏû\ØÓdLm ApXÕ G§oØÓdLmG]lTÓ¡\Õ.

YhP ApXÕ úLôQ CVdLm (Circular orAngular motion) (TPm 7)

JÚ ùTôÚs AfûN ûYjÕ ÑZÛmùTôÝÕARu CVdLjûR úLôQ CVdLm (A) YhPCVdLm Guß ùNôp¡ú\ôm.

ERôWQm

JÚ ùTôÚs YhP TôûR«p CVeÏmùTôÝÕ (`ôlh, AfÑLs, ¡VoþÅpLs,

Ll©Ls (pulleys), ©û[ ÅpLs, ¡ûWi¥eÅpLs) B¡VûYLs JÚ ̈ ûXVô] úYLj§pAfûN Ñt± CVeÏ¡u\].

YhPúLôQ CVdLjûR úLôQj§ûN úYLmGußm ApXÕ ùT¬l©Wp úYLm GußmAûZd¡ú\ôm.

CRu AXÏ ÁhPo /ùNLih(A) úW¥Vu/ùNLih BÏm.

ùTôÚhLs KnÜ ¨ûX Utßm CVdL¨ûX (Bodies at rest and in motion)

©úWd £vPj§p ùRôPo×ûPV LûXfùNôtLs (Terms related to brake system)

JqùYôÚ YôL]j§tÏm R²VôL ©úWdAûUl× Es[Õ. CVeÏm YôL]j§tÏ©úWd úTôhPôp (Ï±l©hP §ûNúYLjÕPu ) CRàûPV §ûN úYLmÏû\¡u\Õ Utßm YôL]j§tÏ G§oØÓdLm HtTÓ¡u\Õ Utßm £±Õ çWmùNu\ÜPu YôL]m ̈ uß®Ó¡u\Õ. G]úY©úWd úTôÓYRtÏ LûXfùNôp≠u ®[dLm¸úZ Lôi©dLlThÓs[Õ.

G§o ØÓdLm (Deceleration) (a) (TPm 8)



85

JÚ Ï±l©hP úSWj§p §ûNúYLmÏû\dLlTÓYÕ. ERôWQm

JÚ Lôôó U¦dÏ 90 ¡úXô ÁhPo úYLj§pùNp¡\Õ AûR 10 ùSô¥L°p¨ßjRlTÓ¡\Õ.

G§oØÓdLm = 90 x x 1/10

= 25 ÁhPo/ùNLih/10 ùNLih

= 2.5 ÁhPo/ùNLih2

G§o ØÓdLj§u úSWm (Deceleration time)

10 ùSô¥ GuTÕ LôûW ̈ ßjÕYRtLô] úUúXÏ±l©hP úSWUôÏm.

¨ßjÕYRtLô] çWm (Stopping distance)

G§o ØÓdLj§uúTôÕ, Lôo SLokR çWmARôYÕ ̈ tTRtLôL GÓjÕdùLôiP çWm‘d’ G] AûZdLlTÓ¡\Õ.

Cß§«p ¨tÏm ùUôjR çWm GuTÕ.NôRôWQUôL ̈ tLdá¥V çWm Utßm Yi¥KhÓTY¬u ùNnúYLj§tÏs Lôo SLÚmçWm B¡VûYLs ùLôiPÕ.

¬Vôdù ûPm ¸úZ ®Y¬dLlThÓs[Õ.

©úWdûL úTôÓmùTôÝÕ, JhÓSo£XúSWeL°p BTj§u RuûUûV EQokÕ©\Ï ©úWdûL úTôÓ¡\ôo. CkR LôXCûPùY°Rôu ¬Vôdù úSWm G]lTÓm.YôL]m ¨tTRtÏ Øu, YôL]m CVeÏm£±Õ çWm Utßm JhÓSo ùNVpTPGÓjÕdùLôs[lTÓm úSWm Cß§«p¨tÏm ùUôjR çWm YôL] Kh¥L°u¬Vôdù úSWjûR ùTôÚjÕ UôßTÓm.¬Vôdù úSWm JhÓSÚdÏ JhÓSoúYßTÓm.

ERôWQm

JÚ Lôôó JÚ U¦dÏ 72 ¡úXô ÁhPôó úYLj§pCVeÏ¡\Õ. ARàûPV ØÓdLm (a) 5ÁhPôó/ùNLih2 Yi¥ KhÓTYôõu ôõVôdùúSWm 1.5 ùSô¥Ls. GqY[Ü çWj§p Yi¥¨tÏm GuTûR LQd¡Ó ùNnL.

¾ôóÜ

Lôôõu §ûN úYLm = 72 kmph

= 20 Á/ùNLih

ØÓdLm = 5 Á/ùNLih2

ùTôÕYô] ¨tÏm çWm

S = (ÁhPô)

¨tÏm GÓjÕd ùLôiP ùUôjR çWm

= 40 ÁhPôó + §ûNúYLm x ôõVôdù çWm

= 40 Á + (20 x 1.5) Á

= 70 ÁhPoLs

¨ëhP²u CVdL ®§Ls (Newon's Law ofMotion)

YôL]eL°p Es[ £X ERôWQeLs

ØRp ®§ (ERôWQjÕPu) First law (withexamples) (TPm 9)

ùTôÚsLs KnÜ ¨ûX«p (A) ºWô]CVdLj§p (Bodies at rest or in Uniform motion)

TDC (A) BDC NPjÕYj§p CÚdÏmùTôÝÕ¼Np CVk§Wj§u ©vPu KnÜ¨ûX«úXVúV CÚdÏm. úLv AÝjRm®ôõ®ûPÙmùTôÝÕ (A) TDC ApXÕ BDC«p CÚkÕ, ©û[ Å≠u úYLj§¦Ü êXm©vPu CVeÏ¡\Õ.

CWiPôm ®§ (ERôWQjÕPu) (Secondlaw (with examples) (TPm 10)

JÚ ùTôÚ°u EkRm Uôßm ÅRm ARuúUp ùNVpTÓm ®ûNdÏ úSôó ®¡Rj§pAûUYúRôÓ Aq®ûN«u §ûN«úXúVCÚdÏm.



86

– CVdLj§p Es[ Lù]d¥e Wôh BDC«pKnÜ ¨ûXdÏ YÚ¡u\Õ.

– Lôt±u ®ûN«u ÅfÑ LôWQUôLYôL]j§u CVdL §ûN UôßTôÓAûP¡\Õ.

– YôL]m ¸r úSôd¡ NôõYô] TôûR«pùNpÛm ùTôÝÕ ARu úYLmA§Lôõd¡\Õ.

– YôL]m úUp úSôd¡ NôõYô] TôûR«pùNpÛm ùTôÝÕ ARu úYLm Ïû\¡\Õ.

êu\ôm ®§ (ERôWQjÕPu) Third law (withexamples) (TPm 11&12)

JqùYôÚ ®ûNdÏm ARtÏf NUUô]G§ôó®ûN Juß EiÓ.

GpXô úUp úSôd¡V ®ûN = GpXô¸rúSôd¡V ®ûN

– §ÚÏj çd¡ ¥TWu£Vp -I çdÏ¡\Õ.

– ¡úWu L«ß Cu_öû] -I çdÏ¡\Õ.



87

úYLm Utßm §ûNúYLj§tÏ ùRôPo×ûPV LQdÏLÞm §\]ônÜT«t£LÞm T«t£ 1.9.28

ERôWQeLs (Examples)

• JÚ ùTôÚs 168 ÁhPôó çWm úSôó úLôh¥p21 ùNLi¥p ùNp¡u\Õ. GqY[Ü §ûNúYLj§p ClùTôÚs ùNp¡u\Õ.

§ûNúYLm = LPkR çWm/úSWm

= 168 ÁhPôó/21 ùSô¥Ls

= 8ÁhPôó/ùSô¥

• JÚ W«p, 150 ¡.Á CûPùY° Es[ CWiÓW«p ¨ûXVeLû[ 2 1/2 U¦ úSWj§pLPkÕ ùNp¡\Õ G²p W«≠u NWôNôõ§ûN úYLjûR LôiL.

NWôNôõ §ûN úYLm = LPkR çWm/ GÓjÕdùLôiP úSWm

= 150 ¡Á/2 1/2 U¦ = 52150

25

150×=

Á/U¦

= 60 ¡Á/U¦

• JÚ YôL]m, ºWô] ØÓdLjÕPu, ARu§ûN úYLm 8 ¡Á/U¦ ≠ÚkÕ 24 ¡Á/U¦þI. 4 ùLNihþp AûP¡u\Õ G²pARu ØÓdLjûR LiÓ©¥ UtßmùNLih¥p YôL]m LPkR çWjûRÙmLiÓ©¥.

BWmT §ûN úYLm (u) = 8 ¡Á/U¦ (u)

Cß§ §ûN úYLm (v) = 24 ¡Á/U¦ (v)

GÓjÕdùLôiP úSWm (t) = 4 ùNLih (t)

∴ v = u + at

24 ¡Á/U¦ = 8 ¡Á/U¦ + a x 4 ùNLih

(24 ¡Á/U¦ - 8 ¡Á/U¦ - 16 ¡Á/U¦)

∴ 4a ùNLih = 16 ¡Á/U¦ = 16000 ÁhPôó/3600ùNLih

∴ ØÓdLm (a) = 16000 ÁhPôó/3600 x 4 ùNLih2

∴ ØÓdLm = 1.1 ÁhPo/ùNLih2

∴ LPkR çWm 4a = 4 x 1.1 = 4.4 ÁhPo

• JÚ Lôôó 50 ¡Á/U¦ §ûN úYLj§pùNußùLôi¥Úd¡\Õ. AÕ 45 ùNLi¥p¨ßjRlTÓ¡\Õ G²p ARu G§ôóØÓdLjûR LôiL.

BWmT §ûN úYLm (u) = 50 ¡Á/U¦ (1 ¡Á =1000 ÁhPov)

Cß§ §ûN úYLm (v) = 0 ¡Á/U¦ (1 U¦ =3600ùNLihv)

GÓjÕdùLôiP úSWm (t) = 45 ùNLih

v = u – at

0 = u – at

u = at

50000/3600 ÁhPôó/ùNLih = a x 45 ùNLih

∴G§o ØÓdLm = 50000/3600 x 45 ÁhPôó/ùNLih2

= 0.30 ÁhPôó/ùNLih2

• ×®Dôól× ®ûNVôp, JÚ ùTôÚs úUúXCÚkÕ ¸úZ RûW«p ®ÓYRtÏ JÚùNLih B¡u\Õ. ùTôÚs GqY[ÜEVWj§p CÚkÕ ¸úZ ®ÝkRÕ GußLôiL. g = 9.81 ÁhPôó/ùNLih2.

BWmT §ûN úYLm (u) = 0 ÁhPôó/ùNLih

×®Dôól× ®ûNVôp HtTÓm ØÓdLm = 9.81ÁhPôó/ùNLih2

GÓjÕdùLôiP úSWm (t) = 1 ùNLih

= ut + gt2 0 x 1 ùNLih = x 9.81 Á/ùNLih2

x 12 ùNLih

= 0 x 1 ùNLih c + x 9.81 Á/ùNLih2 x 1

ùNLih2

1 ùNLih2 = 4.905 ÁhPo s = 4.905 ÁhPo

• JÚ ùTôÚs AûNVôUp CÚdÏm ùTôÝÕARu ÁÕ 30 ̈ ëhPu ®ûN ùNVpTÓ¡\Õ.AlùTôÚ°u ̈ û\ 50 ¡úXô. 4 ùNLi¥tÏ©\Ï ùTôÚ°u §ûN úYLjûR LiÓ©¥Utßm LPdÏm çWjûRÙm Utßm ARuØÓdLjûRÙm LôiL.

®ûN (F) = ¨û\ (m) x ØÓdLm (a)

30 ¨ëhPu = 50 ¡úXô x a

3 ¡úXô x ÁhPôó/ùNLih2 = 50 ¡úXô x a


88

∴ ØÓdLm = 3/50 ÁhPôó/ùNLih2

∴ a = 0.06 ÁhPôó/ùNLih2

v = u + at

= 0 + 0.06 ÁhPôó/ùNLih2 x 4 sec = 0.24 ÁhPôó/ùNLih

s = ut + 1/2 at2 = 0 + 1/2 x 0.06 ÁhPôó/ùNLih2 x 16ùNLih2

s = 0.48 ÁhPôó

• úUpúSôd¡ ùNeÏjRôL G±VlTÓmLp≠u §ûN úYLm 120 ÁhPôó/ùNLih (a)úU≠ÚkÕ ¸rúSôd¡ §Úm×YRtÏ ØuAÕ GhÓm A§LThN EVWm LôiL (b)úUúX ùNuß ¸r úSôd¡ YW ùUôjRmGÓjÕd ùLôiP úSWjûRd LôiL. (c)RûWûV ùRôÓm úTôÕ CRu §ûN úYLmGu] GuTûRd LôiL.

Lp≠u BWmT §ûNúYLm = 120 ÁhPôó/ùNLih

Cß§ §ûN úYLm = 0 ÁhPôó/ùNLih

×®Dôól× ®ûNVôp HtTÓm G§ôó ØÓdLm= 10 ÁhPôó/ùNLih2

u2–v2 = 2g.s

∴ 1202 ÁhPôó2/ùNLih2 – 0 = 2 x 10 ÁhPo/ùNLih2 x s

∴ s = 120 x120/2 x 10 ÁhPôó

= 720 ÁhPôó

¸r úSôd¡ YÚmúTôÕ ARàûPV BWmT§ûN úYLm = 0 ÁhPo/ùNLih Utßm×®DolTôp HtTÓm ØÓdLm = 10 ÁhPo/ùNLih2 Utßm LPkR çWm = 720 ÁhPo.

∴ v2– u2 = 2as

v2– 0 = 2 x 10 ÁhPo/ùNLih2 x 720 ÁhPo

∴ v = 120 ÁhPo/ùNLih

úUp úSôd¡ ùNpX GÓjÕdùLôiP úSWmUtßm ARu §ûNúYLm = 0 ÁhPôó/ùNLih= u/g = 120 ÁhPôó/ùNLih/10 ÁhPôó/ùNLih2

= 12 ùNLih

KnÜ ̈ ûX«p CÚkÕ §ûNúYLm 120 ÁhPôó/ùNLih AûPV GÓjÕd ùLôiP úSWm= v/g = 12 ùNLih.

∴ GÓjÕdùLôs[lThP ùUôjR úSWm.

• Gu_õu ©û[ Åp 2800 rpm þp ÑZp¡u\ÕARàûPV úLôQ§ûN úYLjûR úW¥Vu/ùNLi¥p LQd¡ÓL. (TPm 1 & 2)

úLôQ §ûN úYLm (W) = JÚ Ï±l©hPúYLj§p HtTÓm CPlùTVôóf£ (A) úLôQ§ûN«p ÑtßYÕ CRu AXÏ úSWm BÏm.

¾ôóÜ

©û[ Å≠u úLôQ A[Ü §ûN úYLm W= 2πN/60 úW¥Vu/ùNLih [N = 2800rpm]

= 2π x 2800/60 úW¥Vôu/ùNLih.

= 293.3 úW¥Vôu/ùNLih.

• JÚ úUôhPôôó Lôôó NdLWj§u ®hPm 540ª.Á. CÕ 120° úLôQj§p §Úm×¡\ÕG²p. PVôõu JÚ ×s° GqY[Ü çWmSLÚm.

¾ôóÜ

NdLWm JÚ Ñtß ÑtßYRtÏ JÚ 2π úW¥VuBÏm. ARôYÕ, 2π úW¥Vu = 360°

NdLWm 120° úLôQj§p ÑZp¡\Õ,

120° = 120 x 2π/360

= 2.094 úW¥Vuv

PVôõu JÚ ×s° SLôókR çWm S – re

[where r = 270 ª.Á

θ = 2.094 úW¥Vu]

S = 270 x 2.094 ªÁ

JÚ ×s° YhP TôûR«p SLôókR çWm =565.380ª.Á


= 24 ùNLih


89

• Lôôõu ©u NdLWj§u ®hPm 600 ª.Á©u×\ Bd£p 250 rpm þ p CVeÏ¡\Õ.©u×\ NdLWj§u úYLjûR ÁhPôó/ùNLi¥p LiÓ©¥.

¾ôóÜ

YhP úYLm V = ÁhPo/ùNLih

• JÚ Lôôó 72 km/h úYLj§p ùNp¡u\Õ.ARu ØÓdLm 5 ÁhPô/óùNLih2 ARu¨ßjÕm çWjûR LiÓ©¥dLÜm.

ÁhPo/ùNLih

¾ôóÜ

Va (Lôôõu BWmT úYLm) = 72 kmph

= 20 ÁhPôó/ùNLih

= 20 ÁhPo/ùNLih

¨ßjÕm çWm S = (ÁhPo)

ÁhPo

ÁhPo/ùNLih)


1 S = 180 ª.Á

n = 65 (P×svhúWôd)

Vm = _____Á/¨ªPm

(Vm GuTÕ NWôN¬ùYhÓm úYLm)

2 V = 16 Á/¨ªPm

s = 210 ¨ªPm

n = ______

3 (V GuTÕ NWôN¬ùYhÓm úYLm)

n = 22 vhúWôdv(P×s vhúWôd)/¨ªPm

V = 18 Á/¨ªPm

s = ______ ª.Á

4 s = 240 ª.Á

n = 30 (Jod¡evhúWôd)

V = ______ Á/¨ªPm

5 n = 50 Lh¥evhúWôd

V = 32 Á/¨ªPm

d = ______ ª.Á

s = 64 ª.Á

6 n = 3600 rpm

Vm = _____ÁhPo/ùNLih

Vm GuTÕ ©vP²uNWôN¬ úYLm BÏm)

7 Vm = 0.35 .ÁhPo/ùNLih

s = 200 ª.Á

n = ______ rpm

8 s = 650 ª.Á

Vm = 90 Á/¨ªPm

n = ______ rpm

9 Vm1 = 5.2 ÁhPo/ùNLih A§L¬dLlTÓ¡\Õ

Vm2= 6.3 ÁhPo/ ùNLih

A§L¬dLlThP(n)(rpm) = ______ %

10 s = 250 ª.Án = 45 (P×svhúWôd)V = ______Á/¨ªPm

11 Is : Vm = 25 : 1n =_____(P×svhúWôd)Is = úWd ¥WôYpVxm = vhúWôd¡uúYLm / ̈ ªPm



90

Vm = 10 Á/¨ªPm

n = 12.5 / ¨ªPm

úWd ¥WôYp = ______

13 ¡Wôe¡u ®hPm =100 ª.Á

úWd vÀÓ = 12 Á/¨ªPm

¡Wôed 'n'' = _____rpm

14 v®u¥p'n' = 250 rpm

vhúWôd¡u NWôN¬úYLm= 30 Á/¨ªPm

vhúWôd¡u ¿[m= ________ ª.Á

15 Lô¬u úYLm= 90¡úXôÁhPo / aYo

¨ßjR GÓjÕdùLôiP úSWm= 10ùNLih

G§oØÓdLm =________ ÁhPo/ùNLih2

16 Lô¬u úYLm = 80¡úXôÁhPo / aYo

¨ßjR GÓjÕdùLôiP çWm = 60ÁhPo

Lô¬u G§oØÓdLm= ________ ÁhPo/ùNLih2

17 G§oØÓdLm= 4.5ÁhPo/ùNLih2

¨ßjR GÓjÕdùLôiP çWm = 50ÁhPo

Lô¬s §ûN úYLm =________ ¡Á/U¦

18 Lô¬p ùNu\çWm = 600¡úXôÁhPo

GÓjÕdùL ôiPúSWm = 8 U¦ 20¨ªPmNWôN¬ §ûN úYLm =________ ¡Á/U¦

19 NWôN¬ §ûN úYLm= 56.3 ¡Á/U¦

ùNu\ çWm = 464.475 ¡.Á

GÓjÕd ùLôiPúSWm = ______ U¦

20 Lôo NdLWm

n = 720 rpm

YhPY¥Y úYLm =18.84 Á/ùNLih

d = ________

21 úLôQ úYLm

n = 2000 rpm

úLôQ§ûN úYLm =_______ úW¥Vu/ùNLih

TVuTÓjÕ

W = 2πN/60 úW¥Vu/ùNLih

22 ©vP²u §ûN/úYLm

S = 74 ª.Á

n = 4500 rpm

CûP §ûN úYLm = _______ ÁhPo/ùNLih

A§LThN §ûN úYLm = _______ ÁhPo/ùNLih

(©vP²u NWôN¬ úYLm)


12

23 ¨ßjR GÓjRd ùLôiP ùUôjR çWm

(TVuTÓjRÜm = V2/2a)

V = YôL]j§u úYLm= 80 km/hr

G§oØÓdLm = 5 ÁhPo/ùNLih2

Yi¥ JhÓTY¬u ùNVp úYLj§\u = 2 ùNLih

¨ßjR GÓjÕd ùLôiP çWm = _______ ÁhPo


91

úYûX«u AXÏ, §\u Utßm Bt\p, Cu_÷²u Ï§ûWj§\u UtßmCVk§W XôTm T«t£ 1.10.29

F - ®ûN ApXÕ GûP ®ûN, ̈ ëhP²p ( N)

s - ®ûNVôp JÚ ùTôÚs SLÚm çWm

t - úSWm ùNLi¥p

v - úYLm ÁhPo / ùNLih

w - ®ûNVôp JÚùTôÚs úYûX ùNnRp (A)SLÚRp _øpv£p

P - §\u Yôhv£p

Pout - §\u ùY°lTôÓ (Power output)

Pin - §\u EsÇÓ (Power input)

®ûN (Force)

®ûN GuTÕ, JÚ ùTôÚ°u ÁÕ ùNVpThÓAk¨ûXûV Uôtß¡\úRô ApXÕ Uôt\ØVp¡u\úRô AûR ®ûN Gu¡ú\ôm

®ûN = ¨û\ X ØÓdLm

F = Ma

AXÏ (Unit)

®ûN = ¨û\ X ØÓdLm (F = M x a)

= ¡úXô X ÁhPo (kg X m/sec2 )

= 1 ¨ëhPu (SI unit)

¨ëhPu : 1 ¡úXô ¨û\Ùs[ JÚùTôÚ°u ÁÕ ùNVpThÓ, 1 ÁhPo/ ùNLih2 ØÓdLjûR HtTÓjÕm®ûN 1 ¨ëhPu BÏm.

FPS = 1 TÜiÓ X 1 A¥/ùNih2

= 1 TÜiÓ

Cus = 1 ¡Wôm X 1ùN.Á/ ùNLih2

= ûPu

Mks = 1 ¡úXô X 1ÁhPo/ùNLih2

= ¨ëhPu

1 ̈ ëhPu = 105 ûPuv

1 ¡úXô GûP= 9.8 1N (¨ëhPuv)

1 TÜiÓ = 4.448N (¨ëhPuv)

¨ëhPu = 0.225 TÜiÓ

úYûX (Work) (TPm 1)

®ûNVôp ùNnVlTÓYûR úYûX Gu¡ú\ôm.‘F’ Gu\ JÚ ®ûN JÚ ùTôÚ°u ‘S’ çWmSLoYÕ úYûX G]lTÓm.

úYûX (Work done) ‘W’ = F x s.

úYûX = ®ûN«u U§l× x SLÚm çWm

úYûX«u AXÏLs

A¡X EXL RW ¨oQV Øû\ (S.I system)

JÚ ¨ëhPu ®ûNVô]Õ JÚ ùTôÚ°uÁÕ ùNVpThÓ AlùTôÚû[ 1 ÁhPo çWmSLoj§]ôp ùNnVlThP úYûX 1 _øp(Joule)BÏm

BûLVôp _øp = 1 ¨ëhPu x 1 ÁhPo = 1¨ëhPu ÁhPo (Nm)

AúR úTôp 1 _øp = 1 Nm = 105 ûPuv x 100ùN.Á = 107 ûPuv ùN.Á

= 107 Godv

Nôo©Xô AXÏ (Absolute units) (TPm 2)

C.G.S. ùUh¬d Øû\«p úYûX«u AXÏ = 1God = 1 ûPu x 1 ùN.Á

F.P.S ùUh¬d Øû\«p úYûX«u AXÏ = 1×h TÜiPp = 1 TÜiPp x 1 A¥

M.K.S. ùUh¬d Øû\«p úYûX«u AXÏ = 1_øp = 1 ¨ëhPu x 1 ÁhPo


92

YûWVßdLlThP AXÏLs (Derived units)

C.G.S. (ùUhôõd) Øû\«p 1 ¡Wôm GûP x 1ùN.Á = 981 Gôódv

F.P.S. (©ôõh¥x) Øû\«p 1 A¥ TÜiÓ = 981×h TÜiPp

M.K.S. (ùUhôõd) Øû\«p 1 ¡úXô GûP (A) 1¡úXô ®ûN = 981 _øp

Bt\p (Power) (TPm 2)

úYûX ùNnVlTÓm ÅRúU §\u G]lTÓm.

JÚ YôhÓdÏ GÕ NUm Bt\≠u Yôhv = W/t = F.s/t = F x V

M.K.S. (ùUhôõd) Øû\«p AXÏ 1 kgf ÁhPôó/ùNLih JÚ Ï§ûW §\u = 75 ¡úXôÁhPôó/ùNLih ApXÕ 4500 kgf ÁhPôó/¨ªPm.

1Ï§ûW §\u (HP) (ùUhôõd) = 735.5 Yôhv

1Ï§ûW §\u (HP) (©ôõh¥x) = 746 YôhvLs= 0.746 ¡úXô Yôhv

1 ¡úXô Yôhv = 1.34 Ï§ûW §\u (HP)

CVk§WeLs úYûX ùNnYRtÏùNÛjRlTÓm Bt\p (Input) Cu×h Bt\pG]lTÓm. Gk§Wj§p CÚkÕ ¡ûPdÏmBt\p AÜh×h (output) Bt\p G]lTÓm.CVk§Wj§p Es[ Cu×h Bt\ûX®PAÜh×h Bt\p EWôn®u LôWQUôLÏû\YôLúY CÚdÏm. Cu×h Bt\ÛdÏmAÜh×h Bt\ÛdÏm CûPúV Es[ ®¡RmGk§Wj§u §\û]l ùTôÚjRÕ. CÕNR®¡Rj§p á\lTÓ¡\Õ. (TPm 3)

¾ôóUô²dLlThP Ï§ûWj§\u UtßmTVuTÓjRlTÓm Ï§ûWj §\u (IndicatedHorse Power and Brake Horse Power)

JÚ CVk§Wm GqY[Ü §\àPuùNVp×ôõVdá¥VÕ GuTÕ LQd¡Vp ôö§VôLYûWVßdLlThÓ, CVk§Wj§pùTôÚjRlThÓs[ ®TWj RLh¥pÏ±dLlTÓm. CÕúY ¾ôóUô²dLlThPÏ§ûWj §\u G]lTÓm. CûY ÑÚdLUôLI.H.P. G]lTÓm

JÚ CVk§Wm CVeÏmúTôÕ, HtTÓmEWônÜj RûPL[ôp CZkRÕúTôL, Á§TVuTÓjRlTÓm, Ï§ûWj §\û]d Ï±dÏm.CûR ÑÚdLUôL B.H.P G]lTÓm. CÕ I.H.P.§\û] ®P Ïû\YôL CÚdÏm.

®ûNVôp HtTÓm úYûX = ®ûN«u A[Üx ùTôÚs SLoókR çWm

§\u = Total work done / total time taken

Bt\p (Energy)

ùTôÚsLs úYûX ùNnV úRûYVô]§\ûUdÏ Bt\p Guß ùTVôó. CÕ §\uúSWj§tÏ NUUôL CÚdÏm. JÚ ùTôÚ°uBt\p, AÕ ùNnVdá¥V úYûXûVdùLôiÓ A[®PlTÓ¡\Õ. G]úYúYûX«u AXÏL[ôúXúV Bt\pA[®PlTÓ¡\Õ.

Bt\≠u YûLLs (Forms of energy)

CVk§W Bt\p (Mechanical energy), ªu Bt\p(Electrical energy), AÔ Bt\p (Atomic energy),ùYlT Bt\p (Heat energy), J° Bt\p (Lightenergy), úY§ Bt\p (Chemical energy), J≠ Bt\p(sound energy). JÚ YûL Bt\ûX Utù\ôÚYûL Bt\XôL Uôt\Xôm.

Bt\p A¯®uûU ®§ (Law of conservationof energy)

– Bt\ûX BdLúYô ApXÕ A¯dLúYôCVXôÕ.



93

– JÚ ùTôÚ°p Es[ ùUôjR Bt\ÛmA§úXúV CÚdÏm. (TPm 4)

JÚ ùTôÚ°u CÚdÏm ̈ ûX (A) CVdLj§pEs[ ùTôÚ°p APe¡Ùs[ CVk§WBt\p, ¨ûX Bt\XôLúYô (A) CVdLBt\XôLúYô CÚdLXôm.

¨ûX Bt\p (Potential energy)

JÚ ùTôÚ°p úNªjÕ ûYdLlThP ApXÕAlùTôÚs CÚdLdá¥V ¨ûX«uLôWQUôLl ùT\dá¥V Bt\p, ̈ ûX Bt\pG]lTÓm (TPm 4). JÚ ùTôÚ°u ¨û\ ‘h’EVWj§p ûYdLlThÓs[Õ. AûRA¥lTûPVôLd ùLôiÓ ¨ûX Bt\pL¦dLlTÓ¡\Õ. AÕ mgh ApXÕ Wh ApXÕFh ARôYÕ W ApXÕ F CûY ®ûN«uGûPVôÏm ùTôÚû[ ¸úZ ®ÓYRtÏAàU§jRôp Fh I TVuTÓj§ ̈ ûX Bt\ûXLiÓ©¥dLXôm.

ERôWQm

• ùRôh¥«p úRd¡ ûYdLlThP ¿ôó

• AÝjRlThP ÑÚs ®p

CVdL Bt\p (Kinetic energy)

JÚ ùTôÚs CVeÏYRu êXm ùT\dá¥VBt\p, CVdL Bt\p G]lTÓm. JÚùTôÚ°u ̈ û\ ‘m’ KnÜ ̈ ûX«p BWm©jÕ‘F’ Gu\ ®ûN«u êXm ‘s’ çWjûR LPdL ‘v’Gu\ §ûNúYLjûR AûP¡\Õ. CR]ôpùTôÚs ùNnR úYûX = F x s B]ôp F = m x aG]úY ùTôÚs ùNnR úYûX = m x a x s.

B]ôp a x s = Hù]u\ôp ùTôÚs KnÜ

¨ûX«p CÚkÕ ×\lTÓ¡\Õ.

BûLVôp ùTôÚ°u úYûX = .

ùTôÚ°u úYûX = ùTôÚs ùTt\ Bt\p

CVdL Bt\p = .

ùTôÚs ùTt\ Bt\p = ùTôÚ°u úYûX

¨ûX Bt\p = mgh

CVdL Bt\p = mv2

¨ûX Bt\p = CVdL Bt\p (EWônÜR®odLlThPôp).

ERôWQm

• úWô≠e YôL]m (Rolling vehicle)

• ÑZÛm ©û[ Åp (Rotating fly wheel)

• KÓm ¿o (Flowing water)

• ¸úZ ®Ým ùTôÚs (Falling weight)



94

¨ûX Bt\p, CVdL Bt\p Utßm AYt±tÏ ùRôPo×ûPV LQdÏLsUtßm §\]ônÜ T«t£ T«t£ 1.10.30

¨ûX Bt\p (Potential energy)

‘h’ EVWj§p CÚkÕ Ñj§«u RûX ¸úZ®Ý¡u\Õ. .

¨û\ (m) = 10 ¡úXô.

EVWm (h) = 1.4 ÁhPôó

V2 = 2 gs

V2 = 2 x 9.81 x 1.4

V2 = 27.468

V2 = 5.24 Á/ùNLih

= 10 ¡úXô x 9.81 ÁhPôó/ùNLih2 x 1.4 ÁhPo(TPm 1)

= 137.3 ¨ëhPu ÁhPôó ( 1N = 1kg.m/sec2)

úYûX = ®ûN«u U§l× x SLÚm çWm

work done= F x s = 900 x 10 ¨ëhPu ÁhPôó

= 9000 ¨ëhPu ÁhPôó = 9000 _øp

TYo =

• 2000 kgf TÞûY, 2 ÁhPôó /ùNLih úYLj§pEVôójR úRûYVô] Ï§ûWj §\û]LQd¡ÓL. TVàß§\u 70%.

≠lh -I 1 ùNLih¥p EVojR ùNnR úYûX

®ûN = 2000 kgf

úYûX = F x d

§\u

= 4000 w

§\u ùY°lTôÓ = 4000 w

§\u EsÇÓ = §\u ùY°lTôÓ

η =

EsÇÓ §\u = 7.6 HP

• 100 ¡Wôm ̈ û\, 10 ÁhPôó EVWj§p CÚkÕ¸úZ ®Ý¡u\Õ. CR]ôp AlùTôÚÞdÏHtTÓm CVdL Bt\p GqY[Ü. (g «uU§l× ÁhPôó /ùNLih2 G]d ùLôsL.

BWmT §ûN úYLm= 0

LPkR çWm 10 ÁhPôó

Cß§ §ûN úYLm2

=V2 = 2 x a x s = 2 x 10x10 ÁhPôó2//ùNLih2

CVdL Bt\p (K.E) = x 10 ¡úXô x 5.242

= 137.3 ̈ ëhPu ÁhPôó


• JÚ Ll© 900 ¨ëhPu ®ûNÙPu á¥V¨û\ûV 10 ÁhPôó EVWj§tÏj çdL 2¨ªPm GÓjÕd ùLôs¡\Õ. ®ûNVôpHtThP úYûX Utßm Bt\ûXÙmLiÓ©¥.. (TPm 2)

=75 _øp

ùNLih75 Yôhv

ùY°lTôÓEsÇÓ

x 100%

W t

=9000 _øp

120 ùNLih


95

YôL]j§u ̈ ûXVô] úYLjRôp CVdLBt\p A§Lôõd¡u\Õ. (K.E. developed bythe vehicle at a constant speed)

• JÚ Pu GûPÙs[ JÚ úUôhPôo YôL]mU¦dÏ 60 km/hr úYLj§p ùNp¡\Õ. CkRúYLj§p ARu CVdL Bt\ûX LQd¸ÓùNn.

YôL]j§u CVdL Bt\p = mv2

ARôYÕ m = JÚ Pu ApXÕ 1000 ¡úXô

v = 60 km/hr

¾ôóÜ

v þI ÁhPôó/ùNLihPôL Uôt\ AR]ôpSUdÏ ¡ûPlTÕ

( 1km = 1000m)

( 1hour = 3600sec)

YôL]jûR ØÓdLm ùNnÙm ùTôÝÕCVdL Bt\p A§LôõdÏm (K.E.developed bya vehicle during acceleration)

• 1200 ¡úXô ¨û\ Es[ JÚ úUôhPôóYôL]m 36 ¡úXô ÁhPôõp CÚkÕ 48 km/hrdÏ úYLj§tÏ A§LôõdL ØÓdLmùNnVlTÓ¡\Õ. ØÓdLj§u ùTôÝÕHtTÓm A§L CVdL Bt\ûX LQd¡PÜm.

¾ôóÜ

YôL]j§u ¨û\ = 1200 ¡úXô

YôL]j§u CVdL Bt\≠u úYLm 36 ¡Á/U¦.

= x 1200 x 362J

CVdL Bt\p KE= mv2 J

v= 36 ¡Á/U¦ =36 x = 10 Á/ùNLih

YôL]j§u CVdL Bt\p 48 ¡Á/U¦úYLj§p

= x 1200 x 482J ( 1 ¡úXô¡Wôm ÁhPo /

ùNLih2 = 1N)

( 1 ¨ëhPu ÁhPo = 1 _øp)

v= 48 ¡Á/U¦ =48 x= Á/ùNLih

CVdL Bt\p = x1200 x 10 x10=60000J

CVdL Bt\p = x1200 x x =106666.67 J

CVdL Bt\p ®j§VôNm = 106666.67 J - 60000J = 46666.67 J = 46.666 KJ.

YôL] CVdLj§u úTôÕ HtTÓm úYûX(Workdone in vehicle operation)

úUôhPôó YôL]m NôûX«p CVeÏYRtÏùNnÙm CVk§W úYûX CWiÓ YûLVôL©ôõdLlTÓ¡\Õ.

– IC Cg£u úYLm Utßm TÞûYÙmLY]j§p ùLôiÓ ØÝ Bt\ûXùY«lTÓjR ùNnVlTÓm úYûX.

– úUôhPôó YôL]m TX ®RUô]ùNVpTôÓL°p, NôûX«p DÓTÓmùTôÝÕ ARôYÕ, Ïu±uÁÕHßmùTôÝÕ-/ ØÓdLm /©úWd¡e /CÝjÕf ùNpÛRp (towing) Utßm©uú]ôdÏ ùNpÛRp B¡VYt±pùNnVlTÓm úYûX.



96

§\]ônÜ T«t£ (Assignment)1 ¨û\ (m)= 55 kg

a) s = 1.82 ªhPoGûP (W) = _______øp (joules)b) s = 1.40 ÁhPoGûP (W)= _____øp (joules)c) s = 0.85ÁhPoGûP (W) =_øp(Joules)

2 úSWm(t)= 8 ùNLiha) §\u (P) = _____Yôhvb) §\u (P) = _____Yôhvc) §\u (P) = _____Yôhv

3 GûP (W) = 1312.5_øp¨û\(m) = 350 ¡úXô¡Wômç W m ( s ) = _ _ _ _ _ÁhPo

4 ¨û\ (m) = 75 ¡úXôçWm (s) = 100 metresGûP (W) = ______¨ëhPu ÁhPo§\u (P) = ______Yôhv

5 V = 1 Á3/ùNLihH = 2 Áη = 0.75EsÇÓ §\u =_____ ¡úXôYôhv

6 § \ u ( P ) = 1 2¡úXôYôhvçWm (s) = 4 ÁhPôóúSWm (t) = 20 secs¨û\ (m)=______¡úXô

7 ®hPm (d) = 3 metreEVWm (H) = 2 metreúSWm (t) = 20 minutesçWm (s) = 6 metresP = ______ kWù R ô h ¥ « pR i ½ o¨WlThÓs[ÕTm©e EVWm (s)

8 ®hPm (d) = 200 mmGi¦dûL (n) = 750rpm®ûN (F) = 700¨ëhPu§\u (P) = _____¡úXô Yôhv

9 Cu×h §\u (P) (input) = 4 ¡úXô Yôhv AÜh×h §\u (P) (output)

=3450_øp/ùNLih η = ______ %

10 Ri½¬u L]A[Ü

L] A[Ü (‘V’) = 10metre3

EVWm (H) = 18 metres úSWm (t) = 20 sec η = 70 %(P) AÜh×h (output)= ______ ¡úXôYôh

11 ®hPm (d) = 225 mm çWm (s) = 450 mm© v P ² uAÝjRm

‘P’ = 4.5 bar L] A[Ü (V) = 2.5ÁhPo/ùNLih

(©vPu úYLm) η = 70 % Cu×h §\u

=_____ ¡úXô Yôh

12 TmlùNnVlhPRi½o (‘V’)

= 3 metre3/min

EVWm (H) = 6 metre

η = 0.8

Cu×h §\u

= ______ ¡úXôYôh



97

ùYlTm Utßm ùYlT¨ûX LÚjÕÚ, ùYlTj§u ®û[ÜLs,ùRoúUôÁhPo vúLp, ùNp£Vv, @TôWu aöh, ìUo, ùLp®u UtßmùYlTm Utßm ùYlT¨ûXdÏ CûPúVVô] úYßTôÓLs

T«t£ 1.11.31

ùYlTm (Heat)

ùYlTm GuTÕ JÚ YûL Bt\p. ùYlTBt\ûX úYß Bt\XôL Uôt\Xôm ùYlTmãPô] TÏ§«p CÚkÕ Ï°okR TÏ§dÏSLÚm.

ÑV ùYlT Ht×j §\u (A) ùYlT Gi(Specific heat)

JÚ ùTôÚ°u ÑV ùYlT Ht×j §\u GuTÕJÚ ¡Wôm ¨û\Ùs[ JÚ ùTôÚ°uùYlT¨ûXûV 1°C EVojÕYRtÏúRûYlTÓm ùYlTj§u A[Ü BÏm.

ÑV ùYlT Ht×j §\u ‘s’ Gu\ GÝj§pÏ±l©PlTÓ¡\Õ.

Ri½¬u ÑV ùYlT Ht×j§\u = 1

AÛª²Vm = 0.22

ùNm× = 0.1

CÚm× = 0.12

ùYlT Ht×j §\u (Thermal capacity)

JÚ ùTôÚ°u ùYlT ¨ûXûV 10CEVojÕYRtÏ úRûYVô] ùYlTmAlùTôÚ°u ùYlT Ht×j§\u G]lTÓm.

ùYlT Ht×j§\u = ms LúXô¬

m = ùTôÚ°u ̈ û\ ¡Wôªp

s = ùYlT Gi

LúXô¬@©d U§l× (Calorific value)

JÚ Ï±l©hP ̈ û\Ùs[ JÚ G¬ ùTôÚû[Øt±Ûm G¬dÏm úTôÕ ùY°lTÓm ApXÕEtTj§VôÏm. ùYlTm AlùTôÚ°uLúXô¬@©d úYpë (Calorific value) G]lTÓm.

¿oNU¨ûX (Water equivalent)

JÚ ùTôÚ°u ¿oNU¨ûX GuTÕ ùTôÚû[1°C ùYlT¨ûXûV EVojRúYô (A )Ïû\dLúYô ùNnÙm úTôÕ AlùTôÚ°pAPe¡Ùs[ ¿Wô]Õ AlùTôÚû[lúTôXúY ùYlTjûR Eh ¡W¡dLúYô (A)ùY°«PúYô ùNn¡\Õ. AÕúYAlùTôÚ°u ¿oNU¨ûX G]lTÓm.

¿oNU¨ûX = ¨û\ x ùYlT Gi

G]úY (Water equivalent = Mass of the substance xspecific heat of the substance)

ùYlTj§u YûLLs (Types of heat)

1 EQWlTÓm ùYlTm (Sensible heat)

2 Es Uû\ ùYlTm (Latent heat)

ùYlTj§u AXÏLs (Units of heat)

LúXô¬ (Calorie)

JÚ ¡Wôm ̈ û\Ùs[ ¿¬u ùYlT ̈ ûXûV 1°ùNu¥¡úWh (1°C) EVojÕYRtÏ úRûYVôLùYlTm 1 LúXô¬ BÏm.

BTHU: JÚ TÜiÓ ¨û\Ùs[ ¿¬u

ùYlT¨ûXûV 1° TôWuÍhÓdÏ (1°F)EVojÕYRtÏ úRûYVô] ùYlTm 1 BTHUG]lTÓm. (CÕ ©¬h¥x ùRoUp ë²hBÏm)

C.H.U: JÚ TÜih ¨û\Ùs[ ¿¬uùYlT¨ûXûV 1°C EVojÕYRtÏúRûYlTÓm ùYlTm 1 C.H.U G]lTÓm.

_øp (Joule)

_øp GuTÕ S.I. Øû\«p ùYlTj§uAXLôÏm.

1 LúXô¬ = 4.186 _øp

ùYlTj§]ôp HtTÓm ®û[ÜLs (Effectsof heat)

• ùYlT¨ûX Uôt\m (Change in temperature)

• EÚY A[®p Uôt\m (Change in size)

• ¨ûX Uôt\m (Change in state)

• LhPûUl©p Uôt\m (Change in structure)

• CVp©Vp RuûU«p Uôt\m (Change inPhysical properties)


98

1 EQWlTÓm ùYlTm (Sensible heat)

JÚ ùTôÚ[ô]Õ ùYlTjûR CZkúRô (A)Htú\ô Ru ¨ûX Uô\ôUp ùYlT ¨ûX«pUhÓm Uôt\m AûPkRôp AkR ùYlTmEQWlTÓm ùYlTm G]lTÓm. CûRùRoúUô ÁhP¬p LôQlTÓm ùYlT¨ûX®j§VôNjûR ûYjÕ LiLô¦dLXôm.

2 Es Uû\ ùYlTm (Latent heat)

JÚ ùTôÚ[ô]Õ ùYlTjûR CZkúRô (A)Htú\ô ùYlT ¨ûX Uô\ôUp ARu ¨ûXUhÓm Uôt\m AûPkRôp AkR ùYlTmEsUû\ ùYlTm G]lTÓm. C§p HtßdùLôs[lThP ùYlTúUô (A) CZkRùYlTúUô ùTôÚ°p ùYlT¨ûX Uôt\jûRHtTÓjRôÕ.

YûLLs

1 ùTôÚ°u EÚÏR≠u Es Uû\ ùYlTm(Latent heat of fusion of solid)

2 ùTôÚ°u EÚÏR≠u B®VôYRu EsUû\ ùYlTm (Latent heat of vaporisation of solid)

1 ùTôÚ°u EÚÏR≠u Es Uû\ùYlTm (Latent heat of fusion of solid)

1 ¡Wôm ̈ û\Ùs[ JÚ ùTôÚû[ ARu EÚÏ¨ûX«p ùYlT ¨ûX Uô\ôUp Øt±Ûm¿oU ¨ûXdÏ UôtßYRtÏ úRûYVô]ùYlTm AlùTôÚ°u EÚÏR≠u Es Uû\ùYlTm G]lTÓm.

CRu AXÏ LúXô¬/ ¡Wôm

T²dLh¥«u EÚÏR≠u Es Uû\ùYlTm (Latent heat of fusion of ice)

1 ¡Wôm T²dLh¥ûV 00C ùYlT ̈ ûX«úXúVØt±Ûm ¿WôL UôtßYRtÏ úRûYVô]ùYlTm T²dLh¥«u EÚÏR≠u EsUû\ùYlTm G]lTÓm.

T²dLh¥«u Es Uû\ ùYlTm (L) =80 LúXô¬/ ¡Wôm

2 B®VôR≠u Es Uû\ ùYlTm (Latentheat of vapourisation of liquid)

JÚ ¿oUm ARu ùLô§¨ûX«p HtTÓmùYlTm ARû] B®VôdL UhÓúUTVuTÓ¡\Õ. CkR ùYlTm B® ¨ûX«pUû\kÕ CÚlTRôp CÕ B®VôR≠u EsUû\ ùYlTm G]lTÓm.

¿oUj§u B®VôR≠u EsUû\ ùYlTm(Latent heat of vaporisation of water or latent heat ofsteam)

1 ¡Wôm ¿Wô]Õ ARu ùLô§ ¨ûX«pùYlT¨ûX Uô\ôUp Øt±Ûm B®VôRÛdÏúRûYVô] ùYlTj§u A[Ü AkR ¿oUj§uB®VôR≠u EsUû\ ùYlTm G]lTÓm.

B®«u Es Uû\ ùYlTm (L) = 540 LúXô¬/¡Wôm

ùYlT¨ûX (Temperature)

JÚ ùTôÚs ãPôLúYô (A) Ï°of£VôLúYôCÚdÏm ùYlT A[úY ARu ùYlT ¨ûXBÏm. CÕ ùYlTUô²ûVd ùLôiÓA[dLlTÓ¡\Õ.

ùYlT¨ûXûV A[dÏm vúLpLs (Tem-perature Scales)

ùYlT¨ûX CWiÓ ̈ ûXVô] ùW@lTWuv×s°L[ô] Juß Ri½o Eû\Ùm ×s°Utù\ôuß Ri½¬u ùLô§ ¨ûX×s°LÞdÏ CûPúV A[Üj§ÚjRm

(caliberated) ùNnVlTÓ¡\Õ vúLpL°p Es[

AkR ¨ûXl×s°L[ôY].

vúLp Eû\¨ûX ùLô§¨ûXScale Freezing point Boiling point

ùNu¥¡úWh (°C) 0°C 100°C

@TôWuÍh(°F) 32°F 212°F

ùLp®u 273°K 373°K(K)

ìUo (°R) 0°R 80°R

ùYlTm GuTÕ JÚ ®R Bt\p.ùTôÚ°u ãÓ, (A) Ï°of£ ̈ ûXûVÏ±lTÕ ùYlT¨ûXVôÏm. JÚùYlT¨ûX vúLûX Utù\ôÚùYlT¨ûX vúLXôL Uôtß

YRtLô] E\ÜLs

ùLô§¨ûX (Boiling point)

JÚ ùTôÚs ùYlTjRôp §WY ¨ûX«pCÚkÕ YôÙ ̈ ûXdÏ UôßYÕ AlùTôÚ°uùLô§¨ûX G]lTÓm.

Ri½¬u ùLô§ ̈ ûX 1000C.



99

EÚÏ ¨ûX (Melting point)

JÚ ùTôÚs ùYlTjRôp §P ̈ ûX«≠ÚkÕEÚ¡ §WYUôL UôßYÕ ApXÕ §WYmÏ°okÕ §Pl ùTôÚ[ôL UôßYÕAlùTôÚ°u EÚÏ ¨ûX G]lTÓm.

Iv£u EÚÏ ¨ûX 00C


ùYlTm Utßm ùYlT¨ûXdÏ CûPúV Es[ ®j§VôNm

(Difference between heat and temperature)

ùYlTm (Heat) ùYlT¨ûX (Temperature)

1 CÕ JÚ YûL Bt\p ùYlTj§u ̈ ûXûV ùR¬®d¡u\Õ.

2 CRu AXÏ LúXô¬ CRu AXÏ ¥¡¬

3 LúXô¬ ÁhPWôp ùYlTm ùYlTUô²Vôp ùYlT¨ûXA[dLlTÓ¡\Õ A[dLlTÓ¡\Õ

4 CWiÓ ùTôÚhL°u ùYlTjûR CWiÓ ùYlT¨ûXûV áhÓYRuáh¥ ARu ùUôjR ùYlTjûR êXm LXûY«u ùYlT¨ûXûVLQd¡P Ø¥Ùm. LiÓ©¥dL CVXôÕ.

5 JÚ ùTôÚû[ ùYlTlTÓjÕm CWiÓ ùTôÚhL°u ùYlT¨ûX JúWùTôÝÕ ùYlT¨ûX EVoÜdÏ Uô§¬VôL CÚkRôÛm AûYL°uAlTôtThÓ ùYlT A[Ü ùYlT A[Ü ®j§VôNUôL CÚdÏm.A§L¬dÏm.


100

ùYlT¨ûXLû[ ùNu¥¡úWÓ, @TôWu aöh, ìUo, ùLp®u B¡VvúLpL°p Uôt\m ùNnRp T«t£ 1.11.32

1 00 C - I 0F BL UôtßL

100

C

180

32F 00

=−

180100

C32F

00 ×=−

180100

032F0 ×=−

°F = 0 + 32

= 320F

00C = 320F

2 -400 C - I 0F BL UôtßL

100

C

180

32F 00

=−

180100

C32F

00 ×=−

180100

4032F0 ×

−=−

F - 32 = -72

°F = -72 + 32

= -400F

-400C = -400F

3 370 C - I K BL UôtßL

100

273K

100

C 00 −=

°K-273 = C

°K = C + 273

°K = 37 + 273

= 310 K

370C = 310K

4 700 C - I ìUo BL UôtßL

80

R

100

C 00

=

80100

CR0 ×=

5680100

70R0 =×=

700C = 560R

5 -250 F - I 0C BL UôtßL

180

32F

100

C 00 −=

180

3225

100

C −−=

°

100180

57-C0 ×=

31.669

285C0 −=

−=

- 250F = -31.70C

6 98.60 F - I 0C BL UôtßL

100180

32FC

00 ×

−=

100180

3298.6C0 ×

−=

100180

66.6×=

C37180

6660 0==

98.60F = 370C


¸rLiPûYLû[ UôtßL

1 10.50C = ___0F

2 400C = ___0F

3 600C = ___0F

4 800C = ___0F

5 1050C = ___0F

6 -1000C = ___0F

7 770F = ___0C

8 200F = ___0C

9 4280F = ___0C

10 -2100F = ___0C

11 720R = ___0C

12 1430C = ___K

13 3730K = ___0C

14 7460K = ___0F

15 GkR ùYlT¨ûX«p @TôWu aöhùYlTUô²«u A[Ü ùNu¥¡úWÓùYlTUô²«u A[ûYlúTôp CWiÓUPeÏ CÚdÏm.


101

ùYlT¨ûXûV A[dÏm LÚ®Ls, ùYlTUô²«u YûLLs,ûTúWôÁhPo Utßm ùYlT T¬Uôt\m T«t£ 1.11.33

ùYlT Bt\ûX A[®ÓRp (Measuring heatenergy)

Bt\p, úY§«Vp ®û[ÜLs êXm, JXõ,J≠ (A) ªu]ôt\p BL Uôt\lTÓ¡\Õ.B]ôp ùTÚmTôÛm ùYlT Bt\XôL Uôt\lTÓ¡\Õ. CRu êXm GqY[Ü ùYlT Bt\pUôt\lThPÕ GuTûR A[dLXôm.

ùRôPeÏ¡\Õ ARôYÕ -273°. ùYlT¨ûXCûPùY°Ls AúR Uô§¬ CÚdÏm.

∴ 273K = 0°C, 20°C = 273K + 20K = 293K.

LÚ®Ls (Instruments)

ùTôÚsL°p HtTÓm RuûU Uôt\mªuNôWjRôp ùTôÚhL°u ùYiûUVôLG¬¡u\ úRôt\m, ùYlTdL§o ÅNp UtßmEÚÏRp B¡V UôßRûX LQd¡p ùLôiÓLÚ®Ls ùYlT¨ûXûV A[ùYÓjÕT¥lTRtÏ ERÜ¡\Õ.

ùYlT¨ûXUô² (Thermometer)

§Pl ùTôÚs Utßm §WYjûR ùYlTlTÓj§]ôp AlùTôÚs ®¬YûPÙmClTi©û] A¥lTûPVôLd ùLôiÓùYlTUô²Ls AûUdLlTÓ¡u\]. TôRWNm(Mercury) Utßm BpLaôp (alcohol)B¡VûYLs ºWô] A[®p ®¬YûPÙm.ùYlTjûR ùNÛj§]ôp §WYj§u L]A[Ü A§L¬dÏm úTôÕ Utßm úLl©pX¬¥ë©p (capillary tube) §WYm EVo¡u\Õ.ùTôÕYôL CkR YûL ùYlT¨ûXUô²«pTôRWNm TVuTÓjRl TÓ¡\Õ. Hù]u\ôpTôRWNUô]Õ LiQô¥ ¥ë©p JhPôÕ,(K°ÅÑm) 3000c YûW A[dLXôm.

ûTùUhPp (bimetal) ùYlT¨ûX Uô²«uEúXôLm ùYqúYß ùYlT ùTÚdL GiùLôiPÕ. CkR ûTùUhPp, vûTWp (spiral)Y¥®p Yû[dLlThÓ (twisted) CÚdÏm.ùYlT¨ûX EVÚm úTôÕ CÕ ÑÚs ÑÚ[ôLEVÚm.

ùYlTd LXûYûV A[dÏm LÚ®ûV LúXô¬ÁhPo Guß AûZd¡ú\ôm. CÕ EÚû[Y¥®p Es[ Tôj§Wm BÏm. LXdÏm LWi¥(stirrer) ùTôÕYôL ùNm× EúXôLjRôpùNnVlTh¥ÚdÏm.

JÚ LúXô¬ ÁhP¬p ãPô] §P/§WYùTôÚhLû[ Ï°okR ¨ûX«p Es[ §P/§WY ùTôÚsLÞPu LXdÏm ùTôÝÕ,CWiÓ ùTôÚsLÞm ùYlT¨ûXûVAûPÙm YûW ùYlTlT¬Uôt\m ¨LÝm.AúR LúXô¬ ÁhP¬Ûm AúR ùYlT¨ûXA[®tÏ UôßRp HtThÓ CÚdÏm. LXdÏm®§«u T¥,

§P/ §WY ùTôÚ°u CZkR ùYlTm = §P /§WY ùTôÚhL°u HtLlThP ùYlTm +LúXô¬ ÁhP¬p HtThP ùYlTm

⎥⎦

⎤⎢⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤+

rcalorimeteby

edHeat absorb

substance

idsolid / liqu

ed byHeat absorb

liquid

by solid/

Loss of heat

A[®ÓRp (Measurement)

ùYlT¨ûX ùTôÕYôL ¥¡¬ ùNp£V³pA[dLlTÓ¡\Õ. CmØû\«p Ri½¬uEû\ ̈ ûX 0°C Utßm Ri½¬u ùLô§ ̈ ûX100°C Gußm YûWVßdLlThÓs[].ùLp®u ùYlT¨ûX vúLp absolute 0° p

ûTúWôÁhPo (Pyrometer)

TX YûLVô] EúXôL JVÚdÏm Tt\ ûYdÏm×s°dÏm CûPúV ùYlTjûR EiPôdÏmúYôphúPû_ (voltage) A¥lTûPVôLd


102

ùLôiÓ ùRoúUô GXdh¬d ûTúWô ÁhPoAûUdLlTÓ¡\Õ. ùYlT A[®u ×s°dÏmUtßm JV¬u Ï°okR Øû]LÞdÏ CûPúVEs[ ùYlT¨ûX ®j§VôNjûR ùTôÚjÕúYôphúP_ó CÚdÏm. ùNm× EúXôLjRôpùRoúUô Ll×s G≠ùUihv (Thermocoupleelements) AûUdLlTÓ¡\Õ. (600°C YûW«p)(A) ©[ôh¥]m Utßm ©[ôh¥]m þúW¥Vm (platinum-rhodium) (1600°C YûW«p)

úW¥úVNu ûTúWôÁhPo, £YkR ùYlTEúXôLj§u 3000°C YûW Es[ ùYlT¨ûXûV A[dLXôm. Ï®dLlThP ùRoUpúWvûN (thermal rays) Bl¥Lp ùXuv êXUôLùRoúUô G≠ùUihÓdÏ (thermo element)@lúTôdLv ùNnV úYiÓm. CmÁhP¬uvúLpLs ¥¡¬ ùNp£Vv (A) ùLp®uAX¡tÏ A[Üj§ÚjRm ùNnVlTÓ¡u\].

ùYlTm TWÜRp êuß YûL°pSûPùTß¡\Õ.

• ùYlTd LPjRp (By Conduction)

• ùYlTf NX]m (By Convection)

• ùYlTd L§o ÅNp (By Convection)

ùYlTdLPjRp (Conduction)

JÚ ùTôÚs Rôu ùTt\ ùYlT Bt\ûXêXd áßLs CPm ®hÓ CPm ùTVWôUpAYt±u CVpTô] ¨ûX«p CÚkÕùLôiúP ùYlTjûR TWYf ùNnÙm Øû\úVùYlTdLPjRp G]lTÓm. ùYlTd LPjRpEúXôLeL°p ¨LÝm. ùTôÚ°uêXdáßL°u SLoúYô ApXÕ Uôt\úUôHÕªu± ùYlTm JÚ Øû]«p CÚkÕUtù\ôÚ Øû]dÏ TWÜm. ùTôÕYôL ªuLPj§Ls JÚ SpX ùYlTd LPj§VôÏm.Utßm SpX ùYlTLôl×Ls SpXªuLPjRôl ùTôÚ[ôÏm. JÚ SpXùYlTLôl×lùTôÚs EVoùYlT¨ûXûVRôeL úYi¥V AY£VªpûX.

ùYlTm TWÜRp (Transmission of Heat)

ùYlTm JÚ YûL Bt\p Utßm úYûXùNnÙm RuûU EûPVÕ. ùYlT¨ûX A§LùYlTm Es[ ùTôÚ°p CÚkÕ RôrYô]ùYlTm Es[ ùTôÚÞdÏ TWÜ¡u\Õ. (A)ùYlT¨ûX A§LUôL Es[ ùTôÚ°≠ÚkÕùYlT¨ûX RôrYôL Es[ ùTôÚÞdÏùYlTm TWÜm ¨Lrf£úV ùYlTm TWÜRpG]lTÓm. ùYlT¨ûX A§L ®j§VôNmCÚkRôp ùYlTm úYLUôL TWÜm.

ùYlTf NX]m (Convection)

ùYlTm AûPkR êXdáßLs K¬Pj§pCÚkÕ Utù\ôÚ CPj§tÏ úUpúSôd¡SLoYRu êXm ùYlTm TWÜm Øû\ ùYlTfNX]m G]lTÓm. Ck¨Lrf£ §WYlùTôÚhL°Ûm YôÙlùTôÚhL°Ûm¨Lr¡\Õ. ERôWQm: ÅhÓ ÑÓ Ri½oØû\,úUôhPôo Lô¬u á≠e £vPm.



103

ùYlTd L§o ÅNp (Radiation)

ùYlTm K¬Pj§p CÚkÕ Utú\ôo CPj§tÏGq®R FPLj§u ER® CpXôUpGXdhúWôþ úUd]¥d úYq (electro-magneticwaves) êXm TWÜ¡u\Õ. CmØû\ ùYlTdL§o ÅNp G]lTÓm. CkR AûXVô]Õ K°AûX Utßm Yôù]ô≠ AûX úTôu\RôÏm.ùXuv êXUôL §Úl×Rp Utßm LiQô¥êXm ©W§T≠jRp, Ck¨LrÜdÏ Gq®RùTôÚs FPLØm úRûY«pûX. ERôWQm.ã¬V²PªÚkÕ éªdÏ ùYlTm TWÜm Øû\.

ùYlTm TWÜRp êuß YûL«pSûPùTß¡u\Õ. AûY ùYlTdLPjRp, ùYlTf NX]m, UtßmùYlTd L§o ÅNp.

ùYlTjRôp ®¬YûPRp (Expansion due toheat)

§Pl ùTôÚs, §WYm ApXÕ YôÙdLû[ùYlTlTÓj§]ôp AûY ®¬YûPÙmUtßm L] A[Ü A§L¬dÏm AúR úTôpAûYLû[ Ï°of£Vôd¡]ôÛm, AûYÑÚeÏm Utßm ARu L] A[Ü Ïû\Ùm.

ERôWQm: CW«púY RiPYô[j§uCûQl©p £±V CûPùY° CÚdÏm. CÕúLôûP LôXj§p HtTÓm ùYlTjRôp,RiPYô[eLs ®¬YûPÙm. CûR N¬ùNnYRtLôLj Rôu CûPùY° AûUdLlThÓs[Õ. CqYôß CûPùY° CpXôUpCÚkRôp RiPYô[eLs ®¬YûPkÕUtßm Yû[kÕ CW«pLs L®rYRtÏLôWQUôÏm.

£X ùTôÚhLû[j R®W GpXô §PlùTôÚhLÞm, §WYeLs Utßm YôÙdÞm®¬YûP¡u\]. §WYl ùTôÚhLs §PlùTôÚhLû[ ®P áÓRXôLÜm, YôÙlùTôÚhLs §WYl ùTôÚhLû[ ®PáÓRXôLÜm ®¬YûP¡u\].

ùTôÕYôL Ri½ûW 00C ØRp 40C YûWùYlTlTÓj§]ôp Ri½¬u L] A[ÜÏû\Ùm. ARu ©\Ï L] A[Ü A§L¬dÏm.40Cþp HtTÓm BRôWl×s°ûV ûUVUôLdùLôiÓ Ri½ÚPu ùRôPo×ûPV Ut\LQd¸ÓLs ùNnVlTÓ¡\Õ.



104

¿[l ùTÚdL Gi Utßm ARtÏ ùRôPo×ûPV LQdÏLs Utßm§\]ônÜ T«t£ T«t£ 1.11.34

§iU ùTôÚsL°u ùTÚdLm (Expansion ofsolids)

§iU ùTôÚhLû[ ùYlTlTÓjÕm úTôÕ¸rLiP ùTÚdLeLs HtTÓ¡\Õ.

1 ¿[l ùTÚdLm (Linear expansion)

2 TWl× ùTÚdLm (Superficial expansion)

3 TÚU ùTÚdLm (Cubical expansion)

1 ¿[l ùTÚdLm (Linear expansion)

JÚ §PlùTôÚû[ ãPôdÏm úTôÕ ARu¿[m A§LUôYúR ¿[l ùTÚdLm G]lTÓm.AûY ùTôÚ°u ¿[m A§L¬dÏmùYlT¨ûX Utßm ùTôÚs ùNnVlThPEúXôLm B¡VYtû\ ùTôÚjRÕ.

¿[l ùTÚdL Gi (Co-efficient of linear expan-sion)

JÚ ùTôÚ°u ùYlT ̈ ûXûV 1 ¥¡¬ 0CþdÏEVojÕm úTôÕ ARu ¿[j§p HtTÓmªÏ§lTôh¥tÏm ARu BWmT ¿[j§tÏmEs[ ®¡Rm ¿[l ùTÚdL Gi G]lTÓm. α(BpTô) G] Ï±dLlTÓm.

t10C þp §iU ùTôÚ°u ¿[m = l1

t20C þp §iU ùTôÚ°u ¿[m l2

A§L¬jR ùYlT¨ûX = t2 - t10C

A§L¬jR ¿[m = l2 - l1

¿[ ùTÚdL Gi = A§L¬jR ¿[m/BWmT¿[m x ùYlT¨ûX EVoÜ

( )

[ ]ttttlll

ttlll

121

12

121

12

=−−

=

−×−

=

α

α

TWl× ùTÚdL Gi (Co-efficient of superficialexpansion)

JÚ ¥¡¬ 0C ùYlT¨ûX EVoYRôp JÚùTôÚ°u TWlT[®p HtTÓm TWl©uªÏ§dÏm ARu BWmT TWlT[®tÏm Es[®¡Rm TWl× ùTÚdL Gi BÏm. CÕ β(ÀhPô) G] Ï±dLlTÓm.

TWl× ùTÚdL Gi = 2 x ¿[l ùTÚdL Gi

β = 2α

3 TÚUl ùTÚdLm (Cubical expansion)

JÚ §iU ùTôÚ°u ùYlT¨ûX EVÚmúTôÕ ARu TÚUu A§LUô¡\Õ. CûRúVTÚUl ùTÚdLm Gu¡ú\ôm.

TÚU ùTÚdL Gi (Co-efficient of cubicalexpansion)

JÚ §iU ùTôÚ°u ùYlT¨ûXûV 1¥¡¬dÏ EVojÕYRôp HtTÓm TÚUuªÏ§dÏm ARu BWmTl TÚUàdÏm Es[®¡Rm TÚUl ùTÚdL Gi G]lTÓm. CÕ γ(LôUô) Guß Ï±dLlTÓ¡\Õ.

TÚU ùTÚdL Gi= 3 x ¿[ ùTÚdL Gi

γ = 3α


8 ÁhPo ¿[Øs[ EúXôL Lm© 300Cþ«pCÚkÕ 800CþdÏ ùYlTm EVojRlTÓ¡\Õ. CR]ôp 0.84 ª.Á ¿Þm. ¿[lùTÚdL Gi LiÓ©¥?

BWmT ¿[m (l) = 8 ÁhPo

A§L¬jR ¿[m = 0.84 ª.Á

A§L¬jR ùYlT ¨ûX(t) = 80 - 30 = 500C

A§L¬jR ¿[m = l2-l1 = αl1t

Cß§ ¿[m = l2 = l1(1 + αt)

2 TWl×l ùTÚdLm (Superficial expansion)

JÚ §iU ùTôÚs ãPôdLlTÓm úTôÕARu TWlT[Ü A§LUôYûR TWl×lùTÚdLm Gu¡ú\ôm.

A§L¬jR ¿[m¿[l ùTÚdLGi

=BWmT ¿[m X ùYlT¨ûX

EVoÜ

A§L¬jR ¿[m¿[l ùTÚdLGi (α)


EVoÜ

508000

0.84

×=

400000

0.84=

= 2.1 x 10-6 /0C


105

00Cþ ùYlT¨ûX«p JÚ CÚm× TôXm 100ÁhPo. 400C ùYlT¨ûX«p TôXj§u¿[m GqY[Ü CÚdÏm? JÚ ¥¡¬dÏ,¿[l ùTÚdL Gi 12 x 10-6 .

CÚm× TôXj§u BWmT ¿[m = 100 ÁhPo

A§L¬dLlThP ùYlT ¨ûX = 40 - 0 = 400C



EVoÜ

A§L¬jR ¿[m12 X 10-6 =

100 X 40



EVoÜ

100 = L0 (1 + 0.0006)

00C þ«p ¿[m = 99.94 ÁhPo

100 ùN.Á ¿[Øs[ EúXôL Wô¥u (metal-lic rod) A§L¬jR ¿[jûRd LiÓ©¥?ARu ùYlT ¨ûX 25 ¥¡¬ùNu¥¡úW¥≠ÚkÕ 40 ¥¡¬ ùNu¥¡úWPôL A§L¬dLlTÓ¡\Õ. UtßmARu ¿[l ùTÚdÏ Gi 10 x 10-6 / 0C.

BWmT ¿[m = 100 ùN.Á

A§L¬dLlThP ùYlT ¨ûX =40 - 25 = 150C

A§L¬jR ¿[m10 X 10-6 =

100 X 15

A§L¬jR ¿[m¿[l ùTÚdL

Gi (∝) =

BWmT ¿[m X ùYlT¨ûXEVoÜ


A§L¬jR ¿[m = 401001000000

12××

= 0.048 ÁhPo

40 ¥¡¬ ùNu¥¡úWh¥p CÚm× TôXm =

= 100 + 0.048 = 100.048 ÁhPo

300C þ«p EúXôL Lm©«u ¿[m 100 ùN.ÁUtßm 1000Cþ«p ARu ¿[m 100.14 ùN.Á.¿[l ùTÚdL Gi Utßm 00C þp Lm©«u¿[jûRÙm LiÓ©¥?

300 ùNu¥¡úW¥p BWmT ¿[m = 100 ùN.Á

1000 ùNu¥¡úW¥p Cß§ ¿[m = 100 .14ùN.Á

A§L¬jR ¿[m = 0.14 ùN.Á

A§L¬jR ùYlT¨ûX = 100 þ -30 = 700C

00C þ«p ¿[jûRd LiÓ©¥dL

L1 = L0 (1 + αt)

100 = L0 (1 + 2 x 10-5 x 30)



EVoÜ

¿[l ùTÚdÏ Gi (α) = 10 x 10-6/0C

A§L¬dLlThP ¿[m = 10 x 10-6 x 100 x 15

A§L¬dLlThP ¿[m = 0.015 ùN.Á

20 ¥¡¬ ùNu¥¡úW¥p EúXôL Õi¥u¿[m 2.5 ÁhPo. ARu ¿[l ùTÚdÏ Gi10.4 x 10-6 ¥¡¬ ùNu¥¡úWh Gu\ôp, AÕ¿[YôhPj§p 0.54 ª.Á ¿[m A§L¬jRôpARu ùYlT ¨ûXûVd LiÓ©¥?

BWmT ¿[m = 2.5 ÁhPo

= 2500ª.Á

A§L¬jR ¿[m = 0.54 ª.Á

BWmT ùYlT ¨ûX = 200C


106

0.5410.4 X 10-6 =

2500 X A§L¬jR ùYlT ¨ûX


Cß§ ùYlT¨ûX = 20 + 20.77

= 40.770C


¿[l ùTÚdL Gi (Co-efficient of linear expan-sion)

1 100 Á ¿[Øs[ Lm© 200C -p CÚkÕ 1000C-dÏ ùYlTlTÓjÕm ùTôÝÕ AdLm©100.14 Á ¿[j§tÏ ®¬YûP¡\Õ G²pLm©«u ¿[l ùTÚdL GiûQdLiÓ©¥.?

2 3.6 Á ¿[Øs[ Lm© 1200C ùYlT¨ûXdÏEVojRlTÓ¡\Õ. Lm©«u ¿[lùTÚdLGi 0.00024/0C G²pA§L¬jR Lm©«u¿[m GqY[Ü?

3 6 Á ¿[Øs[ Lm©ûV 1200C ùYlT¨ûXdÏEVoj§]ôp A§L¬jR Lm©«u ¿[mGqY[Ü? Lm©«u ¿[l ùTÚdL Gi10x10-6/0C.

4 100 ùNÁ ¿[Øs[ Lm©ûV 400CùYlT¨ûX«p CÚkÕ 900C ùYlT¨ûXdÏEVoj§]ôp Lm©«u ¿[m GqY[ÜA§L¬jÕ CÚdÏm. CÚm©u ¿[l ùTÚdLGi 10x10-6/0C.

5 150C -p ûUdúWô ÁhP¬u Ã¥e¨ûXlTÓjRlThÓ Es[Õ (standardised)AÕ 350C -p 20.20 ªÁ -VôL JÚ A[ûYLôh¥]ôp, EiûUVô] Ã¥e GqY[Ü?

ûUdúWô ÁhP¬u ¿[lùTÚdL Gi11 x 10-6/0C.

2500 X 10.4 X 10-6

0.54A§L¬jR ùYlT

¨ûX

=


107

ùYlT CZl× Utßm ùYlT Ht× LQdÏLs Utßm §\]ônÜ T«t£T«t£ 1.11.35

LXl× ùYlT CVp (Mixing of heat) m1 = ØRp ùTôÚ°u ¨û\

s1 = ØRp ùTôÚ°u ùYlT Gi

m2 = CWiPôYÕ ùTôÚ°u ̈ û\

s2 = CWiPôYÕ ùTôÚ°u ùYlT Gi

tm = LXûY«u ùYlT ¨ûX

m = ¨û\

Q = ùYlT A[Ü

δt/Δt = ùYlT¨ûX úYßTôÓ

tm = LXûY«u ùYlT ¨ûX

ùYlTj§u AXÏ (Unit of amount of heat)

ùYlTj§u Y¯ ̈ ûX AXÏLs (derived unit) S.I.Øû\«p ùYlTj§u AXÏ _øp BÏm.

ùYlT Gi (Specific heat)

1 ¡úXô ¡Wôm ¨û\Ùs[ JÚ ùTôÚ°uùYlT ¨ûXûV 1 ¥¡¬ EVojÕYRtÏúRûYVô] ùYlTm AlùTôÚ°u ùYlTGi G]lTÓm. CRu Ï±ÂÓ C BÏm.

úRûYlTÓm ùYlTm (A)ùYlTj§uùUdLô²dLp NUu = 4186 _øpLs

= 4.2 kj/kg°C.

JÚ ùTôÚ°u ùYlT¨ûXûVEVojÕYRtÏ úRûYVô] ùYlTm (Quan-tity of heat needed for a substance to rise the tem-perature

JÚ ¡úXô ¡Wôm ¨û\Ùs[ JÚ ùTôÚ°uùYlT ¨ûXûV 1°CþdÏ EVojÕYRtÏúRûYVô] ùYlTm, ùTôÚ°u ùYlT Gi‘s’ G]lTÓm. ‘m’ ¡úXô¡Wôm ¨û\Ùs[ JÚùTôÚû[ ùYlTlTÓj§ ‘t’ Gu\ ARu JÚùYlT¨ûX ®j§VôNm A±V


108

úRûYVô] ùYlT A[Ü = m x s x Δt

BûLVôp Q = m x s x Δt

LXûY (Mixing)

ùYlT ¨ûX Uôt\eLs ¨LÝm ùTôÝÕùYlT Uôt\ ̈ LrÜm SûPùTß¡\Õ. EVokRùYlT ̈ ûX«p Es[ JÚ §iUl ùTôÚû[Ïû\kR ùYlT ¨ûX«p JÚ ùTôÚú[ôÓúNojÕ LXdÏm úTôÕ ùYlT ¨ûX A§LmEs[ ùTôÚ°≠ÚkÕ Ïû\kR ùYlT¨ûXùTôÚÞdÏ ùYlTm LPjRlTÓ¡\Õ. CÕCWi¥u ùYlT ̈ ûXÙm NU¨ûXdÏ YÚmYûW ̈ Lr¡\Õ.

EVokR ùYlT ¨ûX«p Es[ ùTôÚsCZdÏm ùYlTm =

Ïû\kR ùYlT ¨ûX«p Es[ ùTôÚsAûPÙm ùYlT Ht×. Utßm ùTôÚ°uTôLj§p HtTÓm ùUôjR ùYlT ¨ûX =

LXûY«u ùYlTj ùRôûL.

ùYlTl ùTôÚs CZdÏm ùYlTm =Ï°of£Vô] ùTôÚs ùTßm ùYlTHt×.

S Gu\ TÏ§«p HtTÓm ùUôjRùYlTm = LXûY«u ùUôjRùYlTm.

m1 x s1 x t1 + m2 x s2 x t2 = (m1s1 + m2s2)tm.

ERôWQm (Example)

Ï°dÏm ùRôh¥«p 15°Cþp 40 ≠hPoRi½o Es[Õ þ A§p 60°Cþp Es[ 80≠hPo Ri½o Ft\lTÓ¡\Õ. CkR Ri½oLXûY«u ùYlT ¨ûX GqY[Ü?

m1 x s1 x t1 + m2 x s2 x t2 = (m1s1 + m2s2)tm.


JÚ ùLôsLXj§p 25 ¡úXô Ri½oEs[Õ. ùLôsLXm Utßm Ri½¬uùYlT¨ûX 250C. Ri½ûW ùLô§¨ûXdÏ ùLôiÓ YW úRûYlTÓm ùYlT¨ûXûVd LiÓ©¥. ùLôsLXj§uùYlTf NU ¿o = 1 ¡úXô

Ri½¬u ̈ û\ (m) = 25 ¡úXô

Ri½o Utßm ùLôsLXj§uBWmT ùYlT ¨ûX = 250C

Ri½o Utßm ùLôsLXj§uCß§ ùYlT ¨ûX = 1000C

A§L¬dLlThP ùYlT ¨ûX (t) = 100 - 25

= 750C

ùYlTf NU¿o (m s) = 1 ¡úXô

ùLôsLXj§tÏ úRûYVô]ùYlTm = m s t

= 25 x 1 x 75

= 1875 ¡úXô LúXô¬ (K.cal)

Required amount of heat to container = m s t= 1 x 75

= 75 K.cal.

úRûYVô] ùUôjR ùYlTm = 1875 + 75

= 1950 ¡úXô LúXô¬ K.cal.

300 ¡Wôm Ri½¬u ùYlT ¨ûX 250CUtßm 200 ¡Wôm Ri½¬u ùYlT ̈ ûX850C. CWiÓm Ju\ôL LXdLlTÓ¡\Õ.CqYôß Ri½ûW LXkR ©\Ï ARuCß§ ùYlT¨ûXûVd LiÓ©¥. C§pùYlT CZl× HÕm CpûX.

i Ri½¬u GûP = 300 ¡Wôm


Cß§ ùYlT ¨ûX = ‘X’ G] ùLôsL

ùYlT Ht× = x - 250C

ii Ri½¬u ̈ û\ = 200 ¡Wôm


ùYlT CZl× = 850C - x

300 ¡Wôm Ri½¬uùYlT Ht× = m s t

= 300 x 1 x (x - 25)

= 300 x -7500 LúXô¬ (cal).

200 ¡Wôm Ri½¬uùYlT CZl× = m s t

= 200 x 1 x (85 - x)

= 17000 - 200 x LúXô¬ (cal)

ùYlT Ht× = ùYlT CZl×



109

300 x -7500 = 17000 - 200 x

300 x + 200 x = 17000 + 7500

500 x= 24500

x= 24500 = 490C

500

Cß§ ùYlT ¨ûX = 490C

200 ¡Wôm ̈ û\Ùs[ 910C ùYlT ̈ ûX«pEs[ NôRôWQ El× 250 ¡Wôm ̈ û\ÙPu130C ùYlT ̈ ûX«p Es[ PoTuûP²pÖûZdLlTÓ¡\Õ. Cß§ ùYlT ¨ûX160C PoTuûPu B«≠u ÑV ùYlTHt×j §\u0.428 G²p, NôRôWQ El©uÑV ùYlT Ht×j §\û] LiÓ©¥.

El©u ̈ û\ (m) = 20 ¡Wôm

BWmT ùYlT ¨ûX (t) = 910C

PoTuûP²u ̈ û\ (m) = 250 ¡Wôm

BWmT ùYlT ¨ûX (t) = 130C

PoTuûP²u ÑVùYlTm (s) = 0.428

LXûY«u Cß§ùYlT¨ûX = 160C

PoTuûP²u ùYlTHt× (Q) = m s t

= 250 x 0.428 x (16-13)

= 250 x 0.428 x 3

= 321 LúXô¬

NôRôWQ El× CZkRùYlTm (Q) = m s t

= 20 x s x (91-16)

= 20 x s x 75

= 1500 s. LúXô¬

ùYlT CZl× = ùYlT Ht×

1500 s = 321

NôRôWQ El©u ÑV ùYlTHt×j §\u (s) = 0.214

JÚ ùNm× LúXô¬ ÁhP¬p, 80 ¡Wôm¨û\Ùs[ Ri½o 200C þp Es[Õ.LúXô¬ ÁhP¬u ¿o NU¨ûX 20 ¡Wôm.AjÕPu Ri½¬u ùYlT ̈ ûX 400C þpEs[ 100 ¡Wôm ¨û\Ùs[ ¿ÚPuCWiûPÙm LXkR ©\Ï ARu ùYlT¨ûX Gu]?

LúXô¬ ÁhP¬p Ri½¬u¨û\ = 80 ¡Wôm

ùYlT¨ûX = 200CLXûY«u Cß§ ùYlT¨ûX = ‘x’ G]d ùLôsL

Ri½¬u EVojRlThPùYlT¨ûX = x - 20

LúXô¬ ÁhP¬u ¿oNU¨ûX = 20 ¡Wôm

úNodLlThP Ri½¬u¨û\ = 100 ¡Wôm

ùYlT¨ûX = 400C

ùYlT CZl× = 40 - x

ùYlT Ht×

LúXô¬ ÁhP¬p ¿o HtßdùLôiP ùYlTm = m s t

= 80 x 1 x (x - 20)

= 80 x -1600

LúXô¬ ÁhPo HtßdùLôiP ùYlTm = m s t

= 20 x (x - 20)= 20 x (-400)

ùYlT CZl×

¿o úNodLlThPRôp HtThPùYlT CZl× = m s t

= 100 x 1 x (40 - x)

= 4000 - 100x

ùYlT Ht× = ùYlT CZl×

80 x -1600 + 20 x -400= 4000 - 100x

100 x -2000 = 4000 - 100x 100x +100x = 4000 + 2000 200x = 6000 x = 6000/ 200

= 30

Cß§ ùYlT¨ûX = 300C



110

15 ¡Wôm ¨û\Ùs[ Iv Lh¥ -80Cþ«pEs[ûR ùLô§dL úRûYlTÓmùYlTjûRd LiÓ©¥? T²dLh¥«uEs Uû\ ùYlTm =336_øp /¡Wôm.¿Wô®«u Es Uû\ ùYlTm = 2268_øp/¡Wôm. IvLh¥«u ÑV ùYlT Ht×j§\u 0.5

Iv¡ë©u ùYlTm

-80CþpCÚkÕ 00C = mct kJ= m x s x 4.2 x t kJ

= 0.015 x 0.5 x 4.2 x 8 kJ

= 0.252 kJ

00C þ«p Es[ Iv Lh¥ûV00C Ri½WôL Uôt\ = m x h s f kJ

= 0.015 x 336 kJ

= 5.04 kJ

00C «p Es[ Ri½ûW1000C þdÏ EVojÕRp = m c t kJ

= 0.015 x 4.2 x 100 kJ

= 6.3 kJ

1000C «p Es[ Ri½ûW1000C þdÏ ¿Wô®VôL Uôt\Üm = m x hsfg kJ

= 0.015 x 2268 kJ

= 34.02 kJ

ùUôjR ùYlTm Q

= 0.252 + 5.04 + 6.3 + 34.02 kJ

®ûP = 45.612 kJ

§\]ônÜ T«t£ (Assignment)Mixing of Heat

1 m = 120 ≠hPo

t 1 = 20°Ct 2 = 85°Cs = 4.2Q = ______ kj

2 m 1 =80 ≠hPo Ri½oó

m 2 =40 ≠hPo Ri½o

t 1 = 10°Ct 2 = 70°Ct m = ______ °C

3 m1 = 25 ≠hPo Ri½oó

t 1 = 12°Ct 2 = 70°Ct m = 33.75°Cm 2 = ______≠hPo

4 m 1 = 100 ¡.Ri½oót 1 = 12°Cm 2 = 50 ¡.G@Ït 2 = 600°C

Ri½¬u ùYlT EVoÜ =_____°C ≠hPo Ri½oó

5 m1 = 250 ≠hPo Ri½oó

m2 = 150 ¡.G@Ï

t1 = 15°Ctm = 70°Ct2 = ______ °C

6 m1 = 20 ≠hPoùU£u B«p

m2 = 30 ¡.G@Ï

t2 = 160°Ctm = 60°CGiùQn - u

APoj§

t1 = ______ °C = 0.91 3cm

gr

7 m1 = 10 ≠hPo

CK g

kj 4.2

1S

°=

CK g

kj 0.46

2S

°=

m2 = 0.5 kgt1 = 18°Ct2 = 780°C

Ri½¬u ùYlT EVoÜ =___°C



111

8 m1 = 60 ¡.Ri½oó

m = 70 LúXô¬ÁhPo ¡Wôªpm2 = 80 EúXôLm ¡Wôªp

t1 = 200Ct2 = 95 0 Ctm = 250Cs = 0.2s1 = 1s2 =_____

9 m1 = 250 B«p ¡Wôªp

t1 = 15oCm2 = 150 ©jRû[

¡Wôªp

t2 = 900Ctm = 25°Cs2 = 0.09 Ri½o

LúXô¬ ÁhPoNU¨ûX = 3 ¡Wôms1 = ______ ¡Wôm

ùYlT CZl× Utßm ùYlT Ht× (Heat lossand heat gain)

1 85.5 ¡Wôm UQûX 200C -«≠ÚkÕ 350C -dÏEVokR úRûYVô] ùYlT A[®û]LiÓ©¥. UQ≠u ùYlT Gi = 0.1.

2 11 ¡úXô/¨ªPm JÓm A[®p Es[ ¿o120C A[®tÏ EVojRlTÓ¡\Õ. G²p 1U¦ úSWj§p GqY[Ü ùYlTmCZdLlTh¥ÚdÏm G] LiÓ©¥.

3 170 ¡Wôm ¨û\Ùs[ ùTôÚû[ 500C -«≠ÚkÕ 800C -dÏ EVojR 510 LúXô¬úRûYlTÓ¡\Õ G²p ùYlT GiûQdLiÓ©¥.

4 500 ¡Wôm ̈ û\Ùs[ EúXôLjÕiÓ 3000CùYlT¨ûX«p 5 ¡úXô GûPÙs[ ¿¬p®Ý¡\Õ, AlùTôÝÕ ARu ùYlTm 300C- -≠ÚkÕ 750C BL EVÚ¡\Õ G²p,EúXôLjÕi¥u ùYlT GiûQLiÓ©¥ (ùYlT CZl× HÕm CpûX).

5 250C ̈ ûX«p Es[ 300 ¡Wôm Ri½ÚPu850C ¨ûX«p Es[ 200 ¡Wôm Ri½oLXdLlTÓ¡\Õ G²p, CkRd LXûY«uCß§ ùYlT¨ûXûVd LôiL. (ùYlTmHÕm ùY°úV\®pûX G]d ùLôsL).

6 400C ¨ûX«p 100 ¡Wôm GûPÙs[Ri½ÚPu 200C ̈ ûX«p Es[ 80 ¡WômGûPÙs[ Ri½o LXdLlTÓ¡\Õ G²p,CkRd LXûY«u ùUôjRùYlT¨ûX«û]d LôiL. (LúXô¬ÁhP¬u Ri¦o NU¨ûX = 20 ¡Wôm).



112

AÝjRj§u LÚjÕÚ Utßm TpúYß Øû\L°p ARu AXÏLsT«t£ 1.11.36

AÝjRm (Pressure)F - ®ûN, EkÕRp

P - AÝjRm

AÝjRj§u LÚjÕÚ

JÚ ®ûN JÚ ùTôÚ°u AXÏ TWl©u ÁÕùNVpTÓm ®û]úV AÝjRm G]lTÓm.

AÝjRm ‘P’ = ®ûN (A) EkÕRp F AXÏTWl× BÏm. (TPm 1)

A - ®ûN ùNVpTÓm R[j§u TWl×

ERôWQm

JÚ §WYm 2Á2 TWl©u ÁÕ 100 N ®ûNùNÛj§]ôp ARu AÝjRm Gu]GuTûRd LiÓ©¥?

®ûN = 100N

TWl× = 2m2

AÝjRm = ?

= 50 N/Á2

§WYj§u ̈ û\Üß ùYlT¨ûX (§WYm/B®VôRp) (Saturation temperature of a fluid (liq-uid/vapour)§WYm, B® ¨ûXdÏ Uôßm ùTôÝÕ JÚÏ±l©hP AÝjRj§p Es[ ùYlT¨ûXBÏm. CeÏ AÝjRm AúR Uô\ô ¨ûX«pûYdLlTÓm ùTôÝÕ, ùYlT ¿dL ùNnØû\B®ûV §WYUôL AúR ¨ûXVô]ùYlT¨ûX«p Uôtßm. CÕ §WYj§u¨û\Üß ¨ûX G] AûZdLlTÓ¡\Õ(§WYm/B®).

AÝjRj§u AXÏ ̈ /Á2 = 1 ̈ /Á2 = 1 TôvLp

CkR AXÏ ªLÜm £±VÕ. (1 ùNÁ TWl©pJÚ D«]ôp HtTÓm AÝjRm). G]úYAÝjRj§tÏ “Tôo ” (bar) AXLôLA±ØLlTÓjRlThPÕ.

1 Tôo = 105 TôvLp

1 Tôo = 1000 ªp≠ Tôo. ( S.I A[Ü Øû\«pAÝjRj§tÏ TôvLp (Pa) Utßm ùUh¬dØû\«p “Tôo” BÏm.

AÝjRj§u RuûULs (Properties of pressure)

1 BZm A§L¬dL A§L¬dL §WYj§uAÝjRm A§L¬dÏm.

2 JÚ Ï±l©hP ×s°«p §WYj§uAPoj§ûV ùTôßjÕ AÝjRmA§L¬dÏm.

3 §WYm ¨ûXVôL CÚdÏm ùTôÝÕ JÚÏ±l©hP ×s°«p AÝjRm GpXô§ûNL°Ûm JúW A[®p CÚdÏm.

4 JÚ ×s°«p §WYj§p úUp úSôd¡VAÝjRØm, ¸r úSôd¡V AÝjRØm NUA[®p CÚdÏm.

§WYj§u ¨û\Üß AÝjRm (Saturationpressure of a fluid)JÚ Ï±l©hP ùYlT¨ûX«p áhÓm (A)Ïû\dÏm ùYlTm, AkR §WYj§uCVp©Vp RuûUûV Uôtß¡\Õ. ùLôÓdLlTÓm ¨ûXVô] AÝjRúU §WYj§u¨û\Üß AÝjRm Guß A±VlTÓ¡\Õ.

¡¬h¥Lp ùYlT¨ûX Utßm AÝjRm(Critical temperature and pressure)GpXô §WYeLÞdÏm (§WYm/YôÙ )A§LThN ùYlT¨ûX Utßm AÝjRmEs[Õ. ARtÏd ¸úZ ùYlTjûR¿d¡]ôúXô ApXÕ áÓRp ùNnRôúXôARu CVp©Vp ¨ûX Uô±®Óm.ùYlT¨ûX/AÝjR¨ûX, ̈ û\Üß ̈ ûXûVRôi¥]ôp, B®ûV Ï°o®jÕ §WYUôLUôt\ CVXôÕ. GkR B® Ï°o®jRp êXm§WYUôL Uôt\ Ø¥VôúRô, AûR YôÙ GußAûZd¡ú\ôm.

úUp¨ûX ùYlTm ùNnVlThP B® (Su-per heated vapour)JÚ B®«u ùYlT¨ûXûV ARu ̈ û\ÜßùYlT¨ûXdÏ úUp ùYlTlTÓjÕmØû\dÏ úUp¨ûX ùYlTm ùNnVlThPB® Guß ùTVo, CÕ Ï±l©hPAÝjRj§p CÚdÏm

AÝjRm (Pressure)

©¬h¥x TÜih/AeÏXm2 lb/in2

FPS AXÏùUh¬d ¡Wôm/ùNÁ2 g/cm2

AXÏ CGSMKS ¡úXô ¡Wôm/ kg/m2

ÁhPo2

NoúYRN ¨ëhPuv/ N/m2

ÑtßLs SI ÁhPo2


113

ùYlT LPjÕm §\u Utßm Lôl× ùTôÚsLs T«t£ 1.12.37

LXl× ùTôÚsLs (Insulating materials)

ùYlTm A§L ùYlT¨ûX«≠ÚkÕ Ïû\kRùYlT¨ûXdÏ ùNpÛm. ùYlTm, ùYlTL§oÅNp , ùYlTdLPjRp, ùYlTfNX]mB¡V Øû\L°p ÑYt±u FPôLúYô, LRÜ,úUtáûW Utßm Ï°o TR]m ùNnVlThPAû\«u LiQô¥dLRÜL°u êXUôLúYôùNpÛm.

CkR YûL ùYlTdLPjRûX RÓdÏmùTôÚsLú[ Lôl×l ùTôÚsLs (insulatingmaterials) Guß AûZdLlTÓ¡u\].

Lôl× ùTôÚsL°u RuûULs (Propertiesof insulating materials)

- ªLd Ïû\kR LPjRp RuûU

- ¾«û] RÓdÏm RuûU

- Ïû\kR A[Ü DWlTRjûR E±gÑmRuûU

- UQªuûU

- úYlTo ùToªVô©≠h¥ (Vapour permeability)

- CXÏYô] GûP

Lôl×l ùTôÚsLû[ úRoÜ ùNnRp(Selection of insulating material)

JÚ N¬Vô] Lôl×l ùTôÚû[ úRoÜùNnYRtÏ ¸rLiP LôW¦Ls ªLAY£VUô] Ju\ôÏm.

Ïû\kR ùYlTdLPjRp RuûU (Lowthermal conductivity)

ùYlTdLPjRp Esú[ ¨LÝm ùTôÝÕARôYÕ ùYlTm ºWôL LPkÕ ùNpÛmùTôÝÕ AkR ùYlT¨ûX ÅQôLôUpØÝûUVôL TVuTÓjÕYRtÏ Ïû\kRùYlTdLPjRp RuûUÙûPV ùTôÚsAûRf Ñt± úRûYlTÓ¡\Õ. AûYVôY]

- ¾«û]j RÓdÏm RuûU

- CVk§W®Vp Eß§j RuûU

- Ïû\kR A[Ü ¿o B®ûV E±gÑm RuûU

- AûUlTRtÏ G°RôL CÚlTÕ

- ®ûX (Cost)

- ûLVôsYRtÏ G°RôL CÚlTÕ

- Ïû\kR ®ûX

Lôl× ùTôÚsL°u YûLLs (Types ofinsulating materials)

¡[ôvÜp, PUF , RdûL AhûP,ùRoúUôúLôp, Lôl× RLÓ, @ûTTo ¡[ôv.

Lôl× ùTôÚsL°u YûLLs (Types ofinsulating materials)

A¥lTûP YûL«Xô] Lôl× ùTôÚsLsGpXôm ùNVtûL Sôo CûZ«]ôúXô (A)ùNpíXo ùTôÚsL°]ôúXô RVô¬dLlTh¥ÚdÏm. ERôWQm - ¡Xôv Ep, vXôdEp -«]ôp ùNnVlThP ÀeLôuùTôÚsLs, BvùTvPôv Utßm TX,CVtûL CûZ ùTôÚsLs, RdûL, TgÑ, WlToÖûW, UWjçs, ùSp Eª, Tô≠ vùP¬u,Tô≠ëìj¾u, ©ú]ôjùRom Utßm TX.TpúYß Lôl× TVu Tôh¥tLô] YûLUtßm ¡ûPdÏm Y¥YeLs ¸rYÚUôß.

¡Xôv Ep (Glass wool)

CÕ TÏ§ §Pm, ùW£u TôiPh vXôl (A)RLÓL[ôL ùYqúYß APoj§L°p¡ûPd¡\Õ. C§p A§L APoj§ùLôiPûY RôeÏjRuûU A§LmEûPVRôLÜm Utßm Ïû\kR LPj§pEûPVRôLÜm B]ôp B®VôRûXAàU§dÏm YûL«Ûm CÚdÏm. úUpêÓYRtÏ YN§VôL CÕ @Tô«p (foil) EPu¡ûPd¡\Õ.

RdûL (Cork)

CÕ AÝjRlThÓ §PUô] ©[ôd BLúUôpÓ (mould) ùNnVlTh¥ÚdÏm. CÕCúXNôL CÚkRôÛm §PUô]Õ, CûRG°RôL WmTj§u êXm ùYhPXôm. CÕ ¿oùNpYûR RÓdÏm B]ôp A§L A[Ü ¿oB®VôLf ùNpYûR AàU§dÏm.

GdvùTiPh Tô≠vùP¬u(ùRoúUôúLôp ) Expanded polystyrene(Thermocole)

CÕ Eß§Vô] TXûLVôL, ÕLsL[ôL, ÏZôn/Yû[Yô] TWl×Lû[ EûPV Y¥Yj§púUôpÓ ùNnÙm YûL«p ¡ûPd¡\Õ. CûRG°RôL WmTj§u êXm ùYhPXôm.úXNô]Õ Utßm Ïû\kR A[ÜùYlTdLPjRûX AàU§dÏm.


114

Tô≠ë¬j§u (Polyurethane)

CÕ §iûUVô] TXûLVôL, ùS°Yô]TXûLVôL ¡ûPd¡\Õ. §WYeLs CkRTWl×L°u ÁÕ ùR°dLlThÓ AûYÖûWYôL Uôß¡\Õ. CqYûL TXûLLsTpúYß LhÓUô] CPeL°pTVuTÓjRlTÓ¡u\].

UWfºYp/UWjçs (Wood shaving/Saw dust)

CÕ G°RôL AUokÕ AûUYRtÏ ùT¬VA[®Xô] RôeÏ ùTh¥LsúRûYlTÓ¡u\]. CÕ Su\ôL LPjÕmUtßm DWjRuûUûV E±gÑm.

©ú]ôjùRom (Phenotherm)

CÕ TXØLTWl×Lû[ EûPV TXûLVôLÜmUtßm, ûTl ùNd`uL°ÛmTVuTÓjRlTÓ¡\Õ. CûR WmTjûRdùLôiÓ G°RôL ùYhPXôm.

Lôl×ùTôÚsLs Utßm RuûULs/®YWd Ï±l×Ls (Insulating materials and prop-erties/specifications)

Ï°oTR]m Utßm Lôtû\ TRlTÓjÕmÕû\«p TXYûLVô] Lôl× ùTôÚsLsTVuTÓjRlTÓ¡\Õ. Sm Ri½oùRôh¥L°p JÚ £X YûLLú[ETúVôLj§p CÚkR].

Cuû\V LôXLhPj§p ¸rYÚm Lôl×ùTôÚsLú[ TWYXôL TVuTÓjRlTÓ¡u\].

- ùRoúUôúLôp

- ¡XôvÜp/Rôo @ùTph

- T@l (Puf)

- @ûTTo ¡Xôv

ùRoúUôúLôp (Thermocole)

CÕ ùTôÕYô] TVuTôh¥p Es[ Lôl×ùTôÚ[ôÏm. CÕ Ïû\kR Utßm A§LAPoj§ YûLL°p ¡ûPd¡\Õ. CRu R¥Uu0.25" ≠ÚkÕ 5" YûW úYßTÓ¡\Õ.

úRûYdÏ HtT TpúYß Y¥YeL°p(moulded shapes) BL ¡ûPd¡\Õ.

ùRoúUôúLôp ùTôÕYôL Ïû\kR A[úYùYlTjûRdLPjÕm (ÏQm ) , CRuLôWQUôL ùYlTm Esú[ YÚYÕRÓdLlTÓ¡\Õ. CÕ Ïû\kR Utßm A§LAPoj§ Lôl× ùTôÚÞdÏ HtT úYßTÓm.

CûR G°RôL NôRôWQ Lj§«]ôpúRûYlThP Y¥Yj§tÏ ùYh¥dùLôs[Xôm. ùRoúUôúLôp Ï°of£/ùYlTm B¡V CWiûPÙm ¿iP úSWmRôeÏm Nd§ EûPVÕ.

Lôl× ùTôÚ°u 'K' LôW¦ ('K' factor)¸rLiPYôß CÚdÏm (ùRoúUôúLôp).

ùRoúUôúLôp (Thermocole)

-0.20 btu/hr Ft2 deg.f°/inch

@ûTTo¡Xôv (Fibreglass)

JÚ YûL Lôl× ùTôÚs, L²UlùTôÚsL[ôp RVô¬dLlTÓ¡\Õ (UQp,úPôúXôûUh, ÑiQôm×d Lp). ùYlT¨ûXúYßTôh¥]ôp @ûTTo¡Xôv Lôl×ùTôÚs ÑÚeÏY§pûX.

CkR YûL Lôl× ùTôÚsLs EVokR ùYlT¨ûXL°Ûm TVuTÓjRlTÓ¡u\]. (450°C(A) 842°F).

Aû\ ãr¨ûX«p Es[LôtßUiPj§≠ÚkÕ @ûTTo¡Xôv DWjûRE±gNôÕ.

¡[ôvÜp (Glass wool)

¡[ôvÜp A§L ùU≠Rô] AÓd¡p Es[ùTôÚ[ôÏm, ùUuûUVô]Õ (EQÚmùTôÝÕ). CÕ TpúYß A[ÜL°p (R¥Uu0.5" ≠ÚkÕ 2.5" YûW) ¡ûPd¡\Õ. CÕùYsû[, UgNs YiQeL°p çsùNnVlThP LiQô¥j ÕLsLú[ôÓLXkÕ CÚdÏm.

¡[ôvÜp -I ûLVôsYÕ BTjRô]ÕUtßm ¾eÏ®û[®dLd á¥VÕ. (êfÑdLôt±u êXm ÑYô£dÏm ùTôÝÕ )GlùTôÝÕm ¡[ôvÜp -I ûLÙûW,Li¦tÏ TôÕLôl× LiQô¥ B¡VYtû\úYûX ùNnÙm ùTôÝÕ TôÕLôl×d LôWQmLÚ§ A¦V úYiÓm. CÕ TpúYßAPoj§L°p ¡ûPd¡\Õ.

¡[ôvÜp -Ls CWiÓ YûL«pETúVôLlTÓ¡u\]. JÚ YûL ¡XôvÜpÏû\kR ùYlT¨ûX EûPV Ï°oTR]m/Lôtß TRlTÓjÕm TVuTôh¥tLôLETúVôLlTÓjRlTÓ¡u\]. Utù\ôÚ YûLùLô§ LXuL°p (ùYlTd Lôl©tLôL)TVuTÓjRlTÓ¡u\].

Lôl× ùTôÚÞdLô] 'K' LôW¦Ls ('K' factor)

¡XôvÜp: 0.230-.27 Btu/Hr ft2 deg. F°/inch.



115

T@l (Puf)Cuù]ôÚ YûL«p Ï°okR Ri½oùLôÓdÏm ùU£²p Es[ GúYôlTúWhPoùRôh¥dÏ ùY°l×\m (evaporator tank's)TVuTÓjRlTÓm Lôl×ùTôÚs BÏm.

CkR YûL Lôl×LÞdÏ CWiÓCWNôV]eLs TVuTÓjRlTÓ¡u\].(IúNôûNVû]Ó -R11). CûY CWiÓm§WY¨ûX«p LiQô¥ Ïl©L°p (Ïû\kRA[Ü ùLôs[[®tÏ) Utßm úLuL°p(A§L A[Ü ùLôs[[®tÏ) ¡ûPd¡u\].

CkR CWiÓ §WYeLÞm (CWNôV]eLs)GlùTôÝÕm Ï°okR ¨ûX«úXúVûYdLlTh¥ÚdL úYiÓm, CûYCWiûPÙm JÚ Tôj§Wj§p (ùLôsLX²p)úNojÕ Su\ôLd LXd¡]ôp AÕ ÖûWVôLUôßm (BWmTj§p ùU≠RôL Es[ÕR¥U]ôL Uô± Cß§«p L¥]Uô¡®Óm)(ùLôsLXàPu Jh¥d ùLôiÓ ®Óm).

ãZlThP (A) êPlThP ùLôsLX²pLôtß ×Ïm YûL«p GkR JÚ CûPùY°CpXôRYôß TôojÕd ùLôs[ úYiÓm.CÕ ÖûWVôL A§L APoj§«pTPok§ÚdÏm Utßm ùY°l×\m JÝeLt\(finish) ùLôi¥ÚdÏm.

T@l (Puf materials) Lôl×Ls TWYXôLRVô¬lTô[oL[ôp TVuTÓjRlTÓYRuLôWQm AÕ ùYlT ¨ûXûV ¿iPúSWj§tÏ RdLûYlTúRVôÏm.

CûRl TVuTÓjÕY§p Es[ AàáXUt\RuûU Gu]ùY²p CkR ùNnØû\«pCWiÓ WNôV]eLû[ LXkRÜPuEP]¥VôL Su\ôL LXd¡®hÓGúYôlTúWhPo Lô«p úUp (A )GúYôlTúWhPo tank -tÏ ùY°l×\mÏû\kR U¦jÕ°L°p Ft±®P úYiÓm.LôXm LPkÕ ®hPôp §WYd LXûY §PUô¡AkR ùLôsLXú] TV]tßl úTôn®ÓmãZp HtThÓ®Óm.

CkR §WYd LûWNûX FtßYRtÏ Øu]ôpGúYôlTúWhPo (tank) ØÝûUVôL UWm/G@ÏúTôo¥]ôp úRûYVô] CûP ùY°®hÓCßd¡ ûYdLlTP úYiÓm.

Pd¥tÏ Lôl× AûUdÏm Øû\ (Methodof laying duct insulation)

Pd¥p DWlTRm ReÏYRtLô] A±Ï±CpûXùV²p, ¡XôvÜp -I TVuTÓjRXôm.Hù]²p CÕ ¾ûVjRÓdÏm Utßm

ùTôÚ[ôRôW A¥lTûP«p £dL]Uô]Õ.G²àm DWlTRm ReÏm ThNj§p¡XôvÜp TVuTÓjÕm ùTôÝÕ £\l×LY]m GÓjÕd ùLôs[ úYiÓm. ØR≠pPdûP Ñt± Ft\lTP úYiÓm (A) RôoTô«]ôp êP úYiÓm. ARu úUp¡XôvÜp JhÓUôß ùNnV úYiÓm. ©\ÏLôl×l ùTôÚû[ Tô≠¾u RôsL[ôp SuÏÑtßYRu êXm, AÕ ùYlTjRÓl× LôlTôLúYûX ùNnÙm. CRu ©\Ï AkRlTWl©uÁÕ £dLu JVo ùUx (chicken wire mesh) ûYjÕAûR ©[ôvPo ùNnYRu êXm £dLu JVoùUx (Reinforcement) BL CÚdÏm.

GdvúTiPÓ Tô≠v¥¬û] G°RôL úUúXAûUdLXôm Utßm AÕ Eß§VôL CÚdÏm.©hÓùUu (RôodLh¥) Pd¥u ÁÕ TWl×mùTôÝÕ AÕ Lôl× ùTôÚs Utßm PdÓdÏCûPúV TûNúTôp Jh¥d ùLôiÓRôodLh¥ CûQkÕ ®Óm, CR]ôp R²VôLùYlTRÓl× ©hÓúUu úLôh¥e¡tÏ úUpúRûY«pûX. CkR Lôl× ùTôÚû[£ùUih Utßm ©[ôvPo (A )EúXôLjRLÓ AûPl× êXm ØÝûUùNnÕ®P Ø¥Ùm.

JlTû] EháûW AûUlTRu úSôdLm(Purpose of false ceiling)TRlTÓjRlThP Lôtß Pd¥u Y¯VôLLôtß diffusers êXUôL Aû\ (A )AWeLj§às ÖûZ¡\Õ. AúSL diffusers LsJlTû] EháûWÙPu CûQdLlThÓs[Rôp A§p TpúYß ®RUô]diffusers Ls TpúYß úRûYdÏ HtT AûUdLlTh¥ÚdÏm. JlTû] úUt áûWTRlTÓjRlThP Lôtû\, §Úm©f ùNpÛmLôtßPu LXdLôUp TôojÕd ùLôs¡\Õ.

§ÚmTf ùNpÛm Lôtß ùTôÕYôL ©É]m(A) §ÚmTf ùNpÛm ùTh¥ ¡¬p Y¯VôL(JlTû] úUtáûW«p) ùNpÛm. ØRp¨ûX«p ¨ßYlTh¥ÚdÏm A§L ThNBt\p Lôt±p LXlTRôp, AkR Lôtû\ UßÑZt£ ùNnYÕ YZdLUô] ùNVXôÏm.G]úY §Úm©f ùNpÛm Lôtß LôtßTRlTÓjÕm Aû\dúL §Úm© GÓjÕYWlTÓ¡\Õ. BûX Aû\«p §ÚmTfùNpÛm Lôtû\ JlTû] úUt áûWdÏm,EiûUVô] áûWdÏm CûPúV Es[CûPùY° êXm ùY°úVtßYÕ YZdLm.CkR CûPùY° ©Ç]m (plenum) BÏm.JlTû] EháûW §ÚmTf ùNpÛm LôtßY¯ Gußm A±VlTÓ¡\Õ.



116

A±ØLm, ªuNôWj§u ETúVôLeLs, Uô≠dëp, AÔ, ªuNôWmRVô¬jRp, ªuú]ôhPm, ªu]ÝjRm, ªuRûP Utßm ARuAXÏLs T«t£ 1.13.38

ªuNôWm GuTÕ JÚ YûL Bt\p. CÕªLÜm TVàs[ JÚ Bt\p BÏm. CûRLiQôp TôodL CVXôÕ. CÕ ®û[®dLdá¥V TpúYß ®û[ÜLû[ ùLôiÓ RôuCûR SmUôp EQW Ø¥Ùm. ªuNôWmTpúYß YûLVô] Bt\p ARôYÕ ùYlTBt\p, úY§ ®û] Bt\p, AÔ Bt\p,CVk§W Bt\p Utßm úRe¡V Ri½o êXmBt\p B¡V Bt\pLû[ UôtßYRu êXmùT\lTÓ¡\Õ.

ªuNôWjûR ×¬kÕ ùLôsYRtÏ AÔ®uLhPûUlûT Su\ôL ×¬kÕd ùLôs[úYiÓm.

A¥lTûP«p AÔ®u SÓ®pEhLÚYô]Õ Es[Õ. A§p×úWôhPôuLs, GXdhWôuLs Utßm¨ëhWôuLs Es[]. CkR GXdhWôuLsGu¡\ ùSL¥q ªuòhPm EhLÚ®uAÔûY Ñt±YÚ¡\Õ. ×úWôhPôu Tô£¥qªuòhPm BÏm.

ªuNôW EtTj§dLô] BRôWeLs (Sourcesof electricity)úThP¬ (Battery)C§p úY§ Bt\Xô]Õ ªu]ôt\XôLUôt\lTÓ¡\Õ. CÕ úRûYlTÓm úTôÕªu]ôt\ûX ùLôÓd¡\Õ. CÕ YôL]eLsUtßm ªu]Ô®p TVuTÓjRlTÓ¡\Õ.

ù_]úWhPo (Generator)CÕ JÚ CVk§Wm. Gk§W Bt\pªu]ôt\XôL Uôt\lTÓ¡\Õ.

LôkRl×Xm Utßm (magnetic field) ªu²VdÏ®ûNdÏm (emf) CûPúV ªu LPj§ ÑZÛmúTôÕ çiÓ¡\Õ. CmØû\ûVlTVuTÓj§ GpXô®RUô] AC Utßm DCù_]úWhPo Bt\ûX Uôtß¡u\Õ.

ERôWQm (E.g)• A]p ªu ̈ ûXVm (Thermal power station)• ¿oªu ̈ ûXVm (Hydro power station)• AÔªu ̈ ûXVm (Nuclear power station)• Lôt\ôûX ªu¨ûXVm (Wind power station)• ã¬V Jüõ ªu ̈ ûXVm (Solar power station)ªuNôWj§u TVuLs (Uses of Electricity)1 ûXh¥e þ ®[dÏLs

2 Íh¥e þ ÍhPo, JYu

3 TYo þ úUôhPôo, @úTu

4 ¥Wôd`u þ GXdhúWô úUô¥qv,ªu çd¡, ¡úWu (crane)

5 RLYp þ ùRôûXúT£, Rk§,T¬Uôt\m Yôù]ô≠, JVoùXv

6 ùTôÝÕ þ £²Uô, Yôù]ô≠,úTôdÏ ¥.® (T.V.)

7 UÚjÕYm þ x -úW, ̀ ôd ¥ÃhùUih8 úY§Vp þ úThP¬ Nôo_õe,

ªuØXôm éÑRp9 LôkRm þ RtLô≠L LôkRm10 ùTô±«Vp þ úUd]¥d Ndv

(Magnetic chucks)Tt\ûYl×, Tt\ûYlûTx -úW ùNnRp

Uô≠dëp (Molecule)GpXô ùTôÚsLÞm £±V Uô≠dëp BpB]ûY. ùTtú\ôo Y¯ (parent) ùTôÚsL°uªLf £±V AÔjÕLsLs Uô≠dëpG]lTÓm. Uô≠dëpLs JúW ®RUô] Y¥YmUtßm RuûU«p CÚdÏm. JqùYôÚUô≠dëÛm ARu Rôn Y¯ CVp©Vp UtßmúY§Vp RuûULû[d ùLôi¥ÚdÏm.

AÔ (Atom)AÔ®p 3 ÕLsLs Es[]. AûYVôY]:i ×úWôhPôu (Proton): AÔ®u

SÓlTÏ§«p AûUkÕs[ GXdhWôu×úWôhPôu G]lTÓm. AÕ AÔ®u¨ëdXv (ûUVdLÚ) G]lTÓm. C§p×úWôhPôu §WYNUm 1840 UPeÏGXdhWôu §WY NUû] ®P L]Uô]RôLCÚdÏm Utßm AÕ ûahW_uAÔÜdÏ NUUôL CÚdÏm. CÕ Tô£h¥eNôo_ó -I Es[Pd¡ CÚdÏm.

ii ¨ëhWôu (Neutron): CÕ AÔ®p¨ëdXv (ûUVdLÚ) Cp Es[ A¥lTûPÕL[ôÏm. CÕ ¨ëdXv -Cp Es[×úWôhPôu EPu úYLUôL ©ûQdLlTh¥ÚdÏm CRtÏ Nôo_ó GÕÜm¡ûPVôÕ. CÕ áíml (coulomb) -u§WYNUû] A§L¬dÏm.

iii GXdhWôu (Electron): CÕ ̈ ûX«pXôRÕ(A) SLÚm GXdhWôu BÏm. CÕ ̈ ëdXv-I TpúYß ÑtßlTôûR«p Ñt± YkÕùLôiúP CÚdÏm. CÕ ùSL¥q Nôo_ó-I ÑUkÕ ùNpÛm. CÕ ûahW_uAÔ§WYNUj§p 1/1240 TeLôL CÚdÏm.


117

CRu Nôo_ 1.6 x 10-19 áíml BÏm.

ªuNôWm GqYôß EtTj§ùNnVlTÓ¡\Õ (How electricity is produced)JqùYôÚ AÔ®u SÓ®Ûm ªuNôWmEs[Õ. CÕ GXdhWôu Y¥Yj§p Es[Õ.C§p ̈ ûXVôL Es[ ÕLsLs ×úWôhPôuGußm SLokÕ ùLôiúP CÚdÏm ÕLsLsGXdhWôu Gußm A±VlTÓ¡\Õ. C§p×úWôhPôu Tô£h¥q Nôo_ó BÏm. ùY°®ûN«u LôWQUôL SLÚm GXdhWôuLsÏû\YúRô (A ) A§L¬lTúRô(×úWôhPôàPu Jl©Óm ùTôÝÕ) ̈ LrkÕARu ©\Ï Rôu CWiÓ Nôo_óLÞmCûQ¡u\]. GlùTôÝÕ ×úWôhPôû]®P GXdhWô²u EtTj§ Gi¦dûLÏû\¡\úRô ARu LôWQUôL Tô£h¥qNôo_ó BL B¡\Õ CúR Uô§¬ ×úWôhPôû]®P GXdhWô²u EtTj§ Gi¦dûLA§L¬d¡\úRô ARu LôWQUôL ùSLh¥qNôo_ó BL B¡\Õ. CkR Y¯ Øû\«pªuNôWm AÔ®u êXm EtTj§ B¡\Õ.

GXdh¬dLp LûX ùNôtLs UtßmAXÏLs (Electrical terms and units)ªuNôWj§u A[ÜLs (Quantity ofelectricity)HRôYÕ JÚ LPj§«u êXmGXdhWôuL°u KhPm JÚ ®]ô¥úSWj§p JÚ LPj§«u ÏßdÏ ùYhÓTWlûTd LPkÕ ùNpÛm GXdhWôuL°uùUôjR A[Ü ‘Q’ GuTÕ Nôo_ó BÏm. Utßm‘t’ GuTÕ GÓjÕd ùLôiP úSWm.

G]úY

I = tQ

Q = I x t

ªuNôWj§u SI AXÏ coulomb G]lTÓm.6.24 x 1018 GXdhWôuLs (úRôWôVUôL) JÚcoulomb BÏm.

áíml (Coulomb)JÚ LPj§«u Y¯úV 1 Bm©Voªuú]ôhPm ùNpÛm úTôÕ 1 ®]ô¥«pARu Y¯úV ùNpÛm ªuNôWj§u A[Ü 1coulomb BÏm.

CÕ Bm©Vo ùNLih (As) GußmAûZdLlTÓm. CRu ùT¬V AXÏ Bm©VoaYo (AH) BÏm.

1 AH = 3600 As (ApXÕ) 3600 coulombªu²VdÏ ®ûN (EMF) (Electro motive force)(EMF): ªu Ñt±p ªuú]ôhPm ùNpYRtÏ

úRûYlTÓm ®ûNúV ªu]ÝjR ®ûNG]lTÓm. CûR ‘E’ Gu\ GÝjRôpÏ±dLXôm. CRàûPV AXÏ úYôph BÏm.

ªu]ÝjR Årf£ (Potential difference) (P.D)ªu Ñt±u CWiÓ ×s°LÞdÏ CûPúVHtTÓm ªu]ÝjR Årf£úV GXdh¬dLpùTôhPuμVp ¥TWuv G]lTÓm. CÕGlùTôÝÕm EMF I ®Pd Ïû\YôLúYCÚdÏm. CRtÏ ùLôÓdLlTÓmªu]ÝjRúU ùTôhPuμVp ¥TWuvBÏm. CRu Ï±ÂÓ V.

úYôphúP_ó (Voltage): CWiÓ ûXuLs (A)úTv Utßm ¨ëhWp B¡V CWiÓdÏmCûPúV Es[ûY GXdh¬dLpùTôhPuμVp úYôphúP_ó G]lTÓm.CRàûPV AXÏ úYôph BÏm.úYôphúPû_ A[dL úYôph ÁhPoTVuTÓjRlTÓ¡\Õ Utßm Nlû[ùPoª]ÛPu CûQVôL CûQdLlThÓs[Õ.

úYôph (Volt): JÚ ê¥V ªu Ñt±p 1 Kmªu RûP«p 1 Bm©Vo ªuú]ôhPmùNpX úRûYVô] ªu]ÝjRm 1 úYôphG]lTÓm.

ªuú]ôhPm (Current): GXdhWôuL°uKhPúU ªuú]ôhPm G]lTÓm. ApXÕJÚ ®]ô¥ úSWj§p JÚ LPj§«u ÏßdÏùYhÓ TWlûTd LPkÕ ùNpÛmGXdhWôuL°u ùUôjR A[Üªuú]ôhPm G]lTÓm. CRu AXÏBm©Vo ∝ CRu Ï±ÂÓ I A[dÏm LÚ®AmÁhPo.

Bm©Vo (Ampere): 6.24 x 1018 GXdhWôuLs,ªuLPj§«u ÏßdÏ ùYhÓ TWlûT LPkÕJÚ ®]ô¥ úSWj§p ùNpÛm ùUôjR A[ÜJÚ Bm©Vo G]lTÓm (A) JÚ ê¥V ªuÑt±p 1 Km ªu RûP«p 1 úYôphªu]ÝjRj§p ùNpÛm ªuú]ôhPm 1Bm©Vo G]lTÓm.

ªu RûP (Resistance): JÚ ªu Ñt±pªuú]ôhPjûR G§ojÕ ̈ tÏm LPj§«uTi× AdLPj§«u ªu RûP G]lTÓm.CRu AXÏ = Km (Ω) ªu RûPûV A[dLKm ÁhPo TVuTÓjRl TÓ¡\Õ.

Km (Ohm): JÚ ê¥V ªu Ñt±p CÚ×s°LÞd¡ûPúV 1 Bm©Vo ªuú]ôhPmùNpÛm úTôÕ 1 úYôph ªu]ÝjRúYßTôÓ CÚdÏúUVô]ôp AkR×s°LÞdÏ CûPúVÙs[ ªu RûP 1 KmG]lTÓm.



118

Kªu ®§, LQdÏLs Utßm V.I.R CûP«Xô] E\ÜLs, ùRôPo ªuÑtßLs Utßm CûQªu ÑtßL°u LQdÏLs T«t£ 1.13.39

Kªu ®§ (Ohm’s law)

U = ªu]ÝjRm úYôph -p

l = ªuú]ôhPm Bm©V¬p

R = ªuRûP Kªp

GkRùYôÚ Øtß ùTt\ ªuÑt±Ûm,ªuNôWj§u A¥lTûP A[ÜÚdLs(ªu]ÝjRm, ªuú]ôhPm Utßm ªuRûP) CûYLs JqùYôußdÏm ̈ ûXVô]ùRôPo×Ls EiÓ.

A¥lTûP U§l×Ls (Basic values)

A¥lTûP GXdh¬dLp U§lÀhûPùR°YôdL CûR ÏZôn Ri½¬uAÝjRjÕPu Jl©PXôm.

Ri½¬u AÝjRm þ G X d h W ô uAÝjRm þ ªu]ÝjRm

Ri½¬u A[Ü þ G X d h W ô uKhPm þ ªuú]ôhPm

ÏZô«u ¿o KhPjûR LÝjÕlTÏ§ûVCßd¡d Ïû\jRp þ GXdhWôuKhPj§tÏ RûP þ ªuRûP

E\ÜLs (Relationships)

ªu RûPûV ¨ûXVôL ûYjÕ®hÓªu]ÝjRjûR A§L¬jRôp ªuú]ôhPmA§L¬dÏm.

I ∝ V

ªu]ÝjRjûR ̈ ûXVôL ûYjÕ®hÓ, ªuRûPûV A§L¬jRôp. ªuú]ôhPmÏû\Ùm.

Kªu ®§ (Ohm’s law)

úUtá±V CWiÓ E\ÜLs êXm SUdÏKªu ®§ ¡ûPd¡u\Õ.

CÕ YN§dLôL CqYôß

GÝRlTÓ¡\Õ.

V = R.I.

Uô\ôR ùYlT¨ûX«p JÚ ØtßlùTt\ ªuÑt±p TôÙmªuú]ôhPUô]Õ ªuAÝjRj§tÏ úSo ®¡Rj§Ûm, ªuRûPdÏ G§o ®¡Rj§Ûm CÚdÏm.

Kªu ®§


119

ERôWQm (Example)

JÚ Tpl 3.6 úYôp¥p 0.2 Bm©Vo ªuNôWmGÓjÕd ùLôs¡\Õ. Tp©p Es[©XùUuh¥p HtTÓm ªuRûPûVLiÓ©¥. ùLôÓdLlThPûY U = 3.6 V Utßml = 0.2 A. Bm©Vo. RþI LiÓ©¥dL.ùLôÓdLlThPûY V = 3.6 úYôph, l = 0.2Bm©Vo.

BLúY, V = 3.6 V and l = 0.2 A.

BûLVôp, V = l x R

Kmv

ERôWQm (Example)

úXml ©XùUu¥p YZeLlThPÕ. 10.8úYôph B]ôp úYôphúP_ó 12 úYôph BLCÚdL úYiÓm G²p úYôphúP_óCZlûT LiÓ©¥. (TPm 5)

úYôphúP_ó CZl× 12V – 10.8 = 1.2V

YZeLlThP úYôphúP_óªu]ÝjR úYßTôÓ Gußá\lTÓ¡\Õ.

ERôWQm (Example)ûP]úUô®p Eh×\ ªu RûP 0.1 Km,ûP]úUô®u úYôphúP_ó 12V. ùY°l×\ªu Ñtß êXm 20 Bm©Vo ªuNôWmùNÛjRlTÓ¡\Õ. G²p ûP]úUô®púYôphúP_ó GqY[Ü ?

¾oÜ

úYôphúP_ó ¥Wôl = ªuú]ôhPm xEsªu RûP

= 20 x 0.1 úYôph

= 2 úYôph

ERôWQm (Example)úThP¬«u Eh×\ ªu RûP 2 Kmv, CkRúThP¬«p 10 Kmv ªu RûPCûQdLlTÓ¡\Õ. CR]ôp 0.6 Bm©VoùT\lTÓ¡\Õ. úThP¬«u EMFþI LiÓ©¥?(TPm 6)

ªu]ÝjR úYßTôÓ = ªuú]ôhP TônÜx ªu RûP (P.D = Current flowing x Resistance)

= 0.6 A x 10Ω

= 6 úYôph

V.D = ªuú]ôhP TônÜ x úThP¬«pEh×\ ªuRûP

= 0.6 x 2 úYôph

= 1.2 úYôph

úThP¬«u EMF = (6.00 + 1.2) úYôph

= 7.2 úYôph

GpXô ªu RûPL°u áhÓj ùRôûLùUôjR ªu RûPdÏ NUm. CmØû\«p ªuRûPLs, ØRp úXô¥u LûP£ Øû]ÙPuCWiPôYÕ úXô¥u BWmT Øû]ÙPuCûQdLlTÓ¡\Õ Utßm GpXôúXôÓLÞm Øû]dÏ Øû] CûQdLlThÓCÚdÏm.

ùRôPo CûQl× Øû\«u AûUl×:

• RûPL°u Y¯úV ùNpÛm ªuú]ôhPmJúW A[YôL CÚdÏm.

• JqùYôÚ úXôÓLÞdÏ CûPúVVô]ªu]ÝjRm RûPL°u A[®túLtTT¡okÕ ùLôs[lTÓm.

ªu RûP CûQl×Ls (Resistanceconnections)

U = ªu]ÝjRm (úYôp¥p)

R = ªuRûP (Kªp)

I = ªuú]ôhP CuPu£h¥(Bm©V¬p)

ùRôPo CûQl× Øû\ (Series Connection)



120

• JqùYôÚ úXôh úYôphúP_õu áhÓùRôûL ùNÛjRlThP úYôphúP_õdÏNUm.

• ªu Ñt±u ùUôjR ªu RûP A§Ûs[RûPL°u áhÓj ùRôûLdÏ NUm.

l = l1 = l2 = ...V = V1+ V2+ ...R = R1+ R2+ ...

CûQ CûQl× Øû\ (Parallel connection)CmØû\«p ªu RûPL°u JjR Øû]LsCWiÓ Ï±l©hP ×s°LÞdÏ CûPúVCûQdLlThÓ CÚdÏm.

CûQ CûQl× Øû\«u AûUl×(Features of parallel connection):• JqùYôÚ úXô¥Ûm ªuú]ôhPm

TônYÕ úXô¥u ªu RûPûVlùTôÚjRRôÏm.

• JqùYôÚ ªu]Ýj§tÏ CûP«Ûs[úXôÓm NU A[®Ûm Utßm AkR ªuÑtßdÏ ùLôÓdLlThP ªu]ÝjRj§tÏNUUôLÜm CÚdÏm.

• ùUôjR ªuRûP«u áhÓ U§l× CûQCûQl× ªu Ñt±p Es[ ªLf£±VªuRûPûVd Lôh¥Ûm £±VRôLCÚdÏm.

• CûQ CûQl× ªuÑt±p Es[ ùUôjRªu RûPL°u G§o ®¡Rm ùUôjR ªuRûPL°u G§o ®¡Rj§u áhÓjùRôûLdÏf NUUôL CÚdÏm.

l = l1 + l2 + ...V = V1 = V2 ...

ERôWQm (Example)4 Kmv Utßm 6 Kmv B¡V CWiÓªuRûPLs CûQ CûQl× Øû\«pCûQdLlThÓs[Õ. ùUôjR ªu RûPûVLiÓ©¥.

(CûQ CûQl×)

BûLVôp

BûLVôp R Kmv = 2.4 Kmv

ERôWQm (Example)2 Utßm 4 Kmv B¡V CWiÓ ªu RûPLs6 úYôph úThP¬«p CûQdLlThÓs[Õ.

þ ùUôjR ªu RûPûV LiÓ©¥

þ ùUôjR ªuú]ôhPm Utßm TÏ§ªuú]ôhPm LôiL.

¾oÜ

ùUôjR ªu RûP

3Ω11=

34=R

4Ω3=

41+2=

41+

21=

R1+

R1=

R1

tot

21tot

I ùUôjRm= I1 + I2 ªuú]ôhPm

B]ôp

I ùUôjRm = 3A+1.5A

= 4.5 Bm©Vo

§\]ônÜ T«t£L°p ùLôÓdLlThPªu RûP«p ©XùUuh Es[ TplUtßm Ut\ ªuú]ôhPjûRTVuTÓjÕm LÚ®Ls ARôYÕ aôou(Horn) ûYlTo (Wiper) úTôu\ YôL]LÚ®LÞm Es[RôLd ùLôs[Üm.



121

ªuNd§, Bt\p Utßm ARu AXÏLs, §\]ônÜ T«t£ UtßmLQdÏLs T«t£ 1.13.40

V - ªu]ÝjRm (Volts) V

i - ªuú]ôhP CuPu£h¥ (Bm©Vov) (Current Intensity) (Ampheres) A

P - §\u (Yôhv, ¡úXô Yôhv) (Power)(Watts, Kilowatts) W, kW

W - úYûX, Bt\p (Yôh aYo, ¡úXô YôhaYo) wh, Kwh

t - úSWm (aYo) h

ùTôÚû[ JÚ ÁhPo çWj§tÏ SLojÕm§\àdÏ 1 Yôh Guß ùTVo.. ªu Ñt±pªu CVdÏ ®ûN, ªu RûPûV G§od¡u\ÕUtßm úYûX ùNn¡\Õ. ªu Ñt±p ùNnÙmúYûXARu ªuú]ôhPm Bm©VûWlùTôÚjRÕ. ªu CVd¡ ®ûN«p JÚ úYôphGuTÕ, JÚ Bm©Vo ªuú]ôhPj§u êXmJÚ Yôh §\û] ùY°lTÓjÕYRôÏm.

G]úY §\u = úYôphúP_ó (x)ªuú]ôhPm

Voltage x CurrentP= U x l

Yôhv£p §\u = ªu]ÝjRm (úYôph) xªuú]ôhPm (Bm©Vo)

Power in Watts = Voltage in Volts x Current in Ampheres

ªu úYûX, Bt\p (Electric work, energy)ªu úYûX (A) Bt\p GuTÕ ªu]ôt\pUtßm GÓjÕd ùLôiP úSWj§u ùTÚdÏùRôûLVôÏm.

Jod Cu Yôh ùNLih = TYo Cu Yôhvx ûPm Cu ùNLih

Work in Watt seconds = Power in Watts x time in sec-onds

W = P x t

1 _øp GuTÕ 1 Yôh x 1 ùSô¥, CÕ ªLf£±VÕ. G]úY 1 Yôh aYo Utßm 1 ¡úXôYôh aYo Gu\ ùT¬V AXÏLsTVuTÓjRlTÓ¡\Õ.

1 W.h = 3600 Yôh ®]ô¥

1 Kwh = 1000 Wh = 3600000 Yôh ®]ô¥

ªu §\u (Electric Power)

CVk§W®Vp ùNVpTôh¥p úYûXùNnVlTÓm ÅRúU §\u G]lTÓm. ªuÑt±p áP ªu §\²u AXÏ 1 Yôh.CVk§W®Vp ùNVpTôh¥p JÚ ®]ô¥úSWj§p, JÚ ¨ëhPu (N) ®ûN«p JÚ

CVk§Wm Utßm ªu A[ÜL°u EYûULs AhPYûQ«p ùLôÓdLlThÓs[Õ(Table of analogies between mechanical and electrical quantities)

CVk§W A[ÜLs AXÏ (Unit) ªu A[ÜLs AXÏ (Unit)(Mechanical quantity) (Electrical quantity)®ûN ('F’) ¨ëhPu (N) ªu]ÝjRm (‘V’) V

m/s ªuú]ôhPm i A

úSWm t ®]ô¥Ls úSWm t ®]ô¥Ls

§\u P = F x v N §\u P = V x i W = V x A

Bt\p = F x v x t j = Nm Bt\p W = V x i x t j = W x s

§ûN úYLm v =CPl ùTVof£

LôXm


122

W = V I= I2 R

= R

V 2

2

2

IWWV

IVR

=

=

=

Ï±l×: ÖLoúYôÚdLô] ªuLhPQm Kwh þp LQd¡PlTÓ¡\Õ.CÕ SôÓ Utßm Uô¨Xj§tÏUô¨Xm UôßThÓ CÚdÏm.

ERôWQm (Example)

1 ªuú]ôhPm 0.25 Bm©Vo Utßmªu]ÝjRm 240 úYôph ®[d¡uBt\p úWh¥eûL LQd¡Ó.

P = V x I

V = 240 úYôph

I = 0.25 Bm©Vo

BûLVôp,

Bt\p = 240 úYôph x 0.25 Bm©Vo

= 60 úYôph Bm©Vo

B]ôp, 1 Yôh = 1 úYôph x 1 Bm©Vo

BûLVôp, Bt\p = 60 Yôhv

2 15 Bm©Vo ªuú]ôhPm 10 Kmvªu RûP Y¯VôL ùNp¡\Õ. NUuTÓjRlThP ªu A[ûY ¡úXôYôh¥p LQd¡Ó.

ùLôÓdLlThPûY

R = 10 Utßm I = 15 Bm©Vo

Bt\p = V x I = I x R x I = I2 x R

BûLVôp,

Bt\p = 152 x 10 = 2250 Yôhv = 2.25 ¡úXôYôhv

3 ûX²p ªu]ÝjRm 200 úYôph,®[dÏ TVuTÓj§V ªuú]ôhPm 0.91Bm©Vo, ®[dÏ 12 U¦úSWm TVuTôh¥p CÚkRÕ. ùLôÓdLlThPúYôph = 200 úYôph

úYûXûV Whþp LQd¡PÜm

V = I R

WRIW

=

=

RWVWRVI

=

=

=

I = 0.91 Bm©Vo

t = 12 U¦ úSWm

BûLVôp

Bt\p = V x I = 200 úYôph x 0.91 Bm©Vo

= 182 Yôhv

BûLVôp,

úYûX = P x t = 182 Yôhv x 12 U¦úSWm

= 2184 Yôh aYo

4 105 ¡úXô Kmv/ 0.08 Bm©Vo G] N¬ùNnVd á¥V ªu RûPVõp Ï±dLlThÓs[Õ. ARàûPV Ï±dLlThPBt\p GqY[Ü?

ùLôÓdLlThPûY,

R = 1.5 ¡úXô Kmv (k Ohms)

I = 0.08 Bm©Vo (A)

P = ûV LiÓ©¥

V = R x I = 1500 ¡. Kmv. 0.08 Bm©Vo (A ) = 120 úYôph

(P = V x I) = 120 úYôph 0.08 Bm©Vo = 9.6Yôhv ARtÏ T§XôL

P = 12.R = (0.08 Bm©Vo A)2

= 1500 Kmv = 9.6 Yôhv



123

5 220 v ªu]ÝjRj§p 110ΩΩΩΩΩ ªu RûPEûPV ªu Cv§¬ ùTh¥ùNVpTÓ¡\Õ. ªu Cv§¬ ùTh¥TVuTÓj§V ªuú]ôhPm UtßmBt\ûX LiÓ©¥

ªu Cv§¬ ùTh¥«u ªu RûP

(R) = 110 Km

ªu]ÝjRm (V)ó = 220 úYôph

ªuú]ôhPm (I) = RV

= 200/110 = 2 Bm©Vo

Bt\p (w) = V x I

= 220 x 2

= 440 Yôh

6 240 úYôphúP_õp SôuÏ 1000 Yôh,Utßm 180 úYôph ÍhPÚm ùRôPoCûQl©p CûQdLlThÓs[Õ.ªuú]ôhPj§u A[Ü 15 Bm©VoG²p ùUôjR §\û]d LiÓ©¥?

CûQl× = ùRôPo

ÍhP¬u Gi¦dûL = 4

ÍhP¬u §\u (W) = 1000 Yôhv

ÍhP¬u ªu]ÝjRm = 180 úYôph

Nlû[ ªu]ÝjRm = 240 úYôph

ÍhP¬u ªu RûP (R) =

=10324

1000180 x 180

=

= 32.4 Kmv

ùUôjR ªu RûP = 32.4 x 4 = 29.6 Kmv

ùUôjR ªuú]ôhPm (I) = RV

= 129.6240

= 1.85 Bm©Vo

ùUôjR §\u (W) = V x I

= 240 x 1.85 = 444 Yôh

7 40 Yôh ÏZp ®[d¡tÏ 0.1 Bm©Voªuú]ôhPm úRûYlTÓ¡\Õ. AÕJüõoYRtÏ GqY[Ü ªu]ÝjRmúRûY?

®[d¡u §\u (W) = 40 Yôh

ªuú]ôhPm (I) = 0.10 Bm©Vo

ªu]ÝjRm (V) = IW

= 0.140

= 400 úYôph

8 15 Ï§ûW Nd§ ùLôiP úUôhPôoSôs JußdÏ 6 U¦ úSWm ÅRm 15SôhLs CVeÏ¡u\Õ. JÚë²h¥tLô] LhPQm 3 ìTôn, G²p.úUôhPôo CVeÏYRtÏ GqY[ÜìTôn BÏm.

úUôhPô¬u §\u (w) = 15 HP

= 15 x 746 = 11,190 Yôh

JÚ Sô°u TVuTôÓ= 11,190 x 6

= 67140 Yôh

= 67.14 ¡úXô Yôh

15 SôhLÞdLô] TVuTôÓ= 67.14 x 15

= 1007 ¡úXô aYo (A) ë²h

JÚ ë²h¥u ®ûX = Rs. 3

ùUôjR TVÉh¥tLô] ®ûX

= 3 x 1007 = Rs. 3021

1 §\]ônÜ T«t£ (Assignment)

1 ªu RûP (R)= 40 Kmv

ªuú]ôhPm (I)= 6.5 Bm©Vo

ªu]ÝjRm (V)= ______ úYôph

2 ªu]ÝjRm (V)= 6 úYôph


ªu RûP(R) = ______ Kmv



124

3 ªu]ÝjRm (V)= 220 úYôph

ªu RûP(R) = 820 Kmv

ªuú]ôhPm (I)= ______ Bm©Vo

4 ªuú]ôhPm (I)= 4.5 Bm©Vo

ªu]ÝjRm (V)= 220 úYôph

ªu RûP(R) = ______ Kmv



ªuú]ôhPm (I)= _____ Bm©Vo

6 ªu]ÝjRm (V)= 110 úYôphªuú]ôhPm (I)= 4.55 Bm©Voªu RûP(R) =_____ Kmv






ªu RûP(R) = ______ Kmv.


= 7.8 Bm©Vo

(ªu]ÝjRm¥Wôl)


2 §\]ônÜ T«t£ (Assignment)1 ªu RûP (R1 )

= 12 Kmv

ªu RûP (R2 )= 22 Kmv

ªu RûP (R3 )= 24 Kmv º¬v

ªu RûP (R) =______ Kmv

2 ªu RûP (R1 )= 15 Kmv

ªu RûP (R2 )= 25 Kmv


ªu]ÝjRm (V1)= ______ úYôph

ªu]ÝjRm (V2)= ______ úYôph

3 ªu]ÝjRm (V)= 220 úYôph(R1 ) = 40 Kmvªu]ÝjRm (V1 )= 100 úYôph(ùRôPoCûQl©p)R2 = ______ Kmv

4 ªu]ÝjRm (V)= 80 úYôph(I) = 2 A(R1)= 30 Kmv(ùRôPoCûQl©p)(R2) = ______ Kmv

5 ªu RûP (R1 )= 6 Kmvªu RûP (R2 )= 12 Kmv

ªu RûP (R3 ) = 18 Kmv CûY êußm CûQ CûQl×L[ôÏm ªu RûP (R) = ______ Kmv



125


ªu RûP (R1,R2,R3)CûQ CûQl×Øû\

ªu RûP (R1)= 12 Kmv


ªu RûP (R3)= ______ Kmv

7 ªu RûP (R1)= 40 Kmv




ªuú]ôhPm (I1)= ______ Bm©Vo

ªuú]ôhPm (I2 )= ______ Bm©Vo

3 §\]ônÜ T«t£

1 TVuTÓjRlThPªuú]ôhPm

(I) = 0.136 Bm©Vo


TYo (P)= _____ Yôhv

2 TYo (P)= 500 Yôhv

(I) = 2.27 Bm©Vo


3 TYo (P)= 750 Yôhv


(I) = ______ Bm©Vo

4 TYo (P)= 60 Yôhv


ªuRûP (W)R = _______ Yôh


ªu RûP (R)= 484 Kmv

TYo (P)= ______ Yôhv

6 TYo (P) = 550 Yôhv

ªu RûP (R)= 22 Kmv


7 TVuTÓj§V TYo(P) = 1.8 ¡úXôYôhv

ªu RûP (R)= 8 Kmv


8 TVuTÓjRlThPTYo ‘P’ = 2 ¡úXôYôhvªu]ÝjRm (V)= 220 úYôph(Íh¥eG≠ùUihªu]ÝjRm)(R) = ____ Yôhv

9 TYo (P) = 100 Yôhv

úSWm (t) = 1U¦úSWm

TVuTÓj§VBt\p = ______¡úXôYôh aYo



126

10 TVuTÓj§VBt\p ‘W’ = 1¡úXô Yôh aYo

TYo (‘P’)= 100 Yôhv

úSWm (t) = ________U¦úSWm

11 Yôhv (W) = 1.5¡úXô Yôh aYo

úSWm (t) = 45 ̈ ªPm

TYo (P) = ______ ¡úXôYôh

12 G]o_õ ÁhP¬uA[ÜLsW1 = 6755.3 kWhA§L¬dLlThPW2 = 6759.8 kWh

úSWm(t) = 45¨ªPm

TYo (P) =______ ¡úXôYôh

13 TVuTÓj§VBt\p (‘P’)= 6.2 ¡úXôYôh

úSWm (t) = 8 U¦úSWm

JÚ ¡úXô YôhU¦ úSWj§tÏ

= 1.25 ìTôn

ùUôjR ®ûX

= ______ ìTôn



TVuTÓj§VBt\p

= 1 ¡úXô YôhaYo

úSWm (t) = ________U¦úSWm



127

LôkR çiPp, Ru ªu çiPp Utßm TWvTW ªu çiÓ§\uUtßm ªu CVdÏ ®ûN EtTj§ T«t£ 1.13.41

LôkR çiPp (Magnetic induction)

JÚ CÚm×j çi¥u AÚúL, LôkRj§û]ùLôiÓ YÚm ùTôÝÕ LôkRj çiPpHtThÓ CÚm×jÕiÓ LôkRUûP¡\Õ.EiûU«p, CÚm×jÕiûP Ruû] úSôd¡CÝdÏm Øu, LôkRm CÚm×jÕi¥u G§oÕÚYj§p çiPûX HtTÓjÕ¡\Õ UtßmG§ùW§o ÕÚYj§u Dol×jRuûULôWQUôL LôkRm CÚm×jÕiûP Ruû]úSôd¡ CÝd¡\Õ. CRtLôL LôkRmCÚm×ÕiûP ùRôP úYi¥VAY£VªpûX.

TpúYß ªu A[®Óm LÚ®L°p TôoLôkReLÞPu ùUuûUVô] CÚm×jÕÚYjÕiÓLs TVuTÓjRlTÓ¡u\].TVuTÓjÕm LôkRj§tÏ JÚ Ï±l©hPY¥Ym ùLôÓlTRtÏ, CqYûLÕÚYjÕiÓLs TVuTÓjÕYÕLôkRjÕiP≠u LÚjÕÚYj§uA¥lûP«XôÏm.

LôkRl×Xj§u ÅfÑ (Intensity of magneticfield)

LôkRl×Xj§p ûYdLlThÓs[ AXÏÕÚYj§p HtTÓm ®ûNVô]ÕLôkRl×Xj§u ÅfÑ G]lTÓm. CÕ “H” Gu\GÝj§]ôp Ï±dLlTÓm. CRu AXÏ Wb/mBÏm.

ªuLôkR çiPp RjÕYm Utßm ®§Ls(Principles and laws of electromagnetic induction )

JÚ ªuLPj§«p Uôß§ûN ªuú]ôhPmùNpÛm úTôÕ TôWúP«u ªu LôkRçiPp ®§ ARtÏ ùTôÚkÕm.

TôWúP«u ªuLôkR çiPp ®§(Faradays’ Laws of Electromagnetic Induction))

TôWúP«u ØRp ®§ (Faraday’s First Law):LôkRd úLôÓLû[ LPj§ ùYhÓYRôúXô,LPj§ûVf Ñt±Ùs[ LôkRd úLôÓLs ARuU§l©Ûm §ûN«Ûm UôßRp AûPkRôúXôLPj§«p ªu CVdÏ®ûN çiPlTÓ¡\Õ.

TôWúP«u CWiPôYÕ ®§ (The SecondLaw): LPj§«p çiPlTÓm ªu CVdÏ®ûN Ï±l©hP úSWj§p LPj§«u úUpHtTÓm LôkRd úLôÓL°u UôßTôh¥uA[®tÏ úSo ®¡Rj§p CÚd¡\Õ.

Cq®WiÓ ®§«uT¥ LPj§«pªuú]ôhPm EiPô¡\Õ.

ûP]ªd ªu]ÝjRm (Dynamically InducedEMF)

úUtLiP ®§Øû\dúLtT çiPlTÓmªu]ÝjRUô]Õ JÚ ¨ûXVô]LôkRl×Xj§p JÚ ªu LPj§ûV ×Xj§tÏùNeÏjRôL SLW ûYlTR]ôúXô, ¨ûXVôLEs[ JÚ ªuLPj§ ÁÕ UôßTÓmLôkRl×XjûR HtTÓjÕYRôúXô, JÚªu]ÝjRjûR HtTÓjR Ø¥Ùm. ̈ ûXVô]LôkRl ×Xj§p SLÚm ªu LPj§ûV ùLôiÓEiPôdÏm ªu]ÝjRj§tÏ ûP]ªdªu]ÝjRm Guß ùTVo. ERôWQm :ù_]úWhPo.

¨ûXVô] ªu]ÝjRm (Statically InducedEMF)

¨ûXVôL Es[ ªuLPj§ ÁÕ UôßThÓdùLôi¥ÚdÏm LôkR×XjûR ùNÛj§ ARuêXm ªu]ÝjRm ùTßYRtÏ ¨ûXVô]ªu]ÝjRm (Statically Induced EMF) Guß ùTVo.ERôWQm: ¥Wôuv@TôoUo.

¨ûXVô] ªu]ÝjRm (Statically InducedEMF): UôßTÓm LôkRl×Xj§u êXm¨ûXjÕs[ JÚ ªuLPj§«p ªu]ÝjRmHtTÓjÕYRtÏ ¨ûX ªu]ÝjRm GußùTVo.

CÕ @TôWúP -«u EMF ®§«u CWiÓYûLVô] ¨ûXVô] ªu]ÝjRm ¸úZ®[dLlThÓs[Õ.

1 Ru çiPp ªu]ÝjRm (Self inducedemf) Lôl©PlThP JúW Lm©fÑÚ°pHtTÓm ªu]ÝjRm.

2 TWvTW çiPp ªu]ÝjRm (Mutuallyinduced emf) AÚLÚúL Es[ Lm©fÑÚ°pJÚ Lm©fÑÚ°p Uôß §ûN ªuú]ôhPmùLôÓjÕ AÓjR Lm©fÑÚ°p AúR Uôß§ûN ªuú]ôhPjûR GÓdÏmØû\VôÏm.

Ru ªu çiPp (Self-induction): LPj§«uY¯VôL Uôß§ûN ªuú]ôhPm ùNÛjÕmúTôÕ LôkRj§ûN«u §ûNVô]ÕUôßTÓ¡\Õ. C§p ªuú]ôhPm TôÙm§ûNÙm LôkRl×Xj§u §ûNûVÙm A±kÕùLôs[ Ø¥Ùm.


128

JÚ ØÝ ûNd¡°p LôkRl×XUô]ÕLPj§ûV Ñt± HtTÓ¡\Õ. CÕG§o§ûN«Ûm §ÚmT HtTÓ¡\Õ.AlùTôÝÕ LôkR×Xj§u ØÝ A[Üm"0"YôL Es[Õ. LôkRd úLôÓL[ô]ÕLPj§ûV ûUVUôLd ùLôiÓ ùY°«pÑtß¡u\]. CkRd úLôÓLs LPj§ûVùYhÓ¡u\].

Ruªu çiPp (Self induction)

TôWúP«u ®§dÏ CQeL LPj§Vpªu²VdÏ ®ûN çiPlTÓ¡\Õ. CúRúTôp LôkRl ×Xj§p ÁiÓm LôkR ®ûNdúLôÓLs LPj§ûV ùYhÓYRôp ÁiÓmJÚ Øû\ ªu²VdÏ ®ûN çiPlTÓ¡\Õ.CRtÏ Ruªu çiPp Guß ùTVo.CmØû\«p HtTÓm ªu²VdÏ ®ûNVô]Õ¨ûXVô] ªu²VdÏ ®ûNVôÏm. (TPm 1)

TWvTW ªuçiÓ §\u (Mutual Inductance):ùTôÕYô] LôkR úLôÓL°]ôp JußApXÕ ARtÏ úUtThP Lô«pLsLôkRj§]ôp CûQdLlThPôp CûYLsTWvTW ªuçiÓ §\u ÏQô§NVeLû[ùTtßs[Õ Guß A±VXôm. CkRA¥lTûP RjÕYj§p ¥WôuvTôoUo,úUôhPôo, ù_]úWhPo Utßm CRW ªuNôR]eLs CVeÏ¡\Õ. TWvTW ªuçiP≠uT¥ JÚ Lô«≠p TôÙmªuú]ôhPjRôp TdLj§Ûs[ Lô«≠pªu]ÝjRm çiPlTÓ¡\Õ.

TPm 2þp Lôi©jÕs[T¥ Lô«p L1 þ²pTôÙm ªuú]ôhPjRôp LôkR UiPXmARû] Ñt± HtTÓ¡\Õ. úUÛm £X LôkRúLôÓLs Lô«p L2 Y¯VôLÜm Tôn¡\Õ.CR]ôp TWvTW ªuçiÓ §\uHtTÓ¡\Õ. Lô«p Ju±u ªuú]ôhPm N1

ÑtßLû[Ùm Lô«p CWi¥u ªuú]ôhPmN2 ÑtßLû[Ùm ùLôiÓs[Õ. CR]ôpTWvTW ªu çiÓ §\u M EiPô¡\Õ.

CWiÓ Lô«pL°Ûm EiPôÏm TWvTWªuçiÓ §\û] 'M' A[dL CWiûPÙmùTôÕYô] Nôlh CÚm× úLôo (soft iron core)ÁÕ ûYjúRô ApXÕ ÑtßdL°uGi¦dûL LQd¡hÓ A±kÕ ùLôs[Xôm.CÕ ¥WôuvTôoU¬p Es[ûRúTôpCÚdÏm.

CWiÓ Lô«pLÞdÏm CßdLUôLûY«i¥e ùNnVlTÓ¡\Õ. AR]ôpÄdúL_ó_ôp HtTÓm CZl× ªLÜm Ïû\Ü.CWiÓ Lô«pLÞdÏ CûPúV LôkRúLôÓL°u CûQl× HtThÓs[Õ GußLÚj§p ùLôiÓ TWvTW ªuçiÓ§\u'M' ûV A±VXôm.

CVdL ªuçiPp §\u (Dynamicallyinduced EMF)

ù_]úWhPo (Generator): CVk§W Bt\ûXªu Bt\XôL Uôtßm CVk§Wm ªuNôWù_]úWhPo BÏm.

ù_]úWhP¬u RjÕYm (Principle of theGenerator): CVk§W Bt\ûX ªu Bt\XôLUôtßm ù_]úWhPo @TôWúP þ®uªuLôkR çiPp ®§«u RjÕYj§uA¥lTûP«p CVeÏ¡\Õ.

@TôWúP®u ªuLôkR çiPp®§(Faraday’s laws of electromagnetic induction):

CWiÓ ®§Ls Es[]

ØRp ®§

• LôkRj úLôÓLû[ LPj§ ùYhÓYRôúXô,LPj§ûVf Ñt±Ùs[ LôkRd úLôÓLsARu U§l©Ûm §ûN«Ûm UôßRpAûPkRôúXô LPj§«p ªu CVdÏ ®ûNçiPlTÓ¡\Õ.

CWiPôm ®§

• LPj§«p çiPlTÓm ªu CVdÏ ®ûNÏ±l©hP úSWj§p LPj§«u úUp



129

HtTÓm LôkRd úLôÓL°u UôßTôh¥uA[®tÏ úSo ®¡Rj§p CÚd¡\Õ.

ªu CVdÏ®ûN«u YûLLs (Types ofemf): @TôWúP ®§L°uT¥, ªu CVdÏ®ûNûV (emf) ̈ ûXVô] LPj§«u UôßThPLôkRl×XjûR CûQlTRu êXúUô (A)LôkRl×Xj§tÏm LPj§dÏm CûPúVE\ÜØû\ SLo®u êXúUô çiP Ø¥Ùm.

CVdLj§u êXm çiPlThP ªuCVdÏ ®ûN (Dynamically induced emf): TPm3a -p Lôh¥Ùs[ T¥ ¨ûXVô]LôkRl×Xj§p Es[ LPj§ SLoYRuêXUôL ªu CVdÏ ®ûN çiPlTPXôm(A) TPm 3b -p Lôh¥Ùs[T¥ ¨ûXVô]LPj§«p LôkRl ×Xj§û] SLojÕYRuêXUôLúYô çiPlTÓm ªu CVdÏ®ûN,CVdLj§u êXm çiPlThP ªu CVdÏ®ûN G]lTÓm.

3a Utßm 3b TPj§p Lôh¥Ùs[ûRl úTôpCWiÓ Øû\«Ûm LPj§ ®ûN«uúLôÓLû[ ùYhÓYRu êXm ªu CVdÏ®ûNûV çiPXôm úUÛm ªu CVdÏ®ûN«u CÚlûT A±kÕ ùLôs[“úLpYú]ô ÁhPo êXm - ‘G p Es[Øs°u ®XLp êXm LiÓ ùLôs[ Ø¥Ùm.CkRj RjÕYm DC Utßm AC ù_]úWhP¬pªuNôWm RVô¬dLl TVuTÓjRlTÓ£\Õ.

¨ûXjRuûU«u êXm çiPlThPªu CVdÏ ®ûN (Statically induced emf):TPm 2 -p Lôh¥Ùs[T¥, JÚ ¨ûXVô]LPj§«u úUp HtTÓm úYßThPLôkRl×Xj§u êXm çiPlTÓm ªuCVdÏ ®ûN, ¨ûXj RuûU«u êXm

çiPlThP ªu CVdÏ®ûN G]lTÓ¡\Õ.C§p LôhPlThÓs[ Lô«p 1 Utßm Lô«p2 Juû\ Juß ùRôhÓd ùLôsY§pûXUtßm AYt±²ûPúV GkR ªu CûQl×mCpûX.

TPm 4 -u T¥ Lô«p 1 -p ETúVôLlTÓjRlTÓm TôhP¬ (DC) Nlû[ êXm Lô«p 2 -pªu CVdÏ ®ûN çiPlTÓ¡\Õ. (Ñ®hf“S” êÓm ùTôÝÕ (A) §\dÏm ùTôÝÕ). JÚúYû[ Ñ®hf -I ¨WkRWUôL ê¥úVô (A)§\kR ̈ ûX«úXô ûYj§ÚkRôp Lô«p 1 -pEtTj§VôÏm LôkRl×Xm ̈ ûXVô]RôL (A)é_ó_÷VUôL CÚdÏm úUÛm Lô«p 2 -p ªuCVdÏ ®ûN çiPlTPôÕ. G]úY DC ªuÑt±p Lô«p 1 -u NôdëªûP êÓYúRô (A)§\lTRu êXm LôkRl×Xm úYßTÓmùTôÝÕ ªu CVdÏ ®ûN çiPlTÓ¡\Õ.

Uô\ôL TPm 4 -p Lôh¥Ùs[T¥ úThP¬Utßm Ñ®hf -I Lô«p 1 -p CÚkÕ ALt±®hÓ AûR AC TYo Nlû[ÙPuCûQjÕ®PXôm. CqY\ôL Lô«p 1 -I ACTYo Nlû[«p CûQlTRôp Lô«p -2 EPuCûQdLlThP Lô«p 1 -p EtTj§ùNnVlTÓm UôßTÓm LôkRl ×Xm, Lô«p -1 AC TYo Nlû[ÙPu CûQdLlThÓs[YûW Lô«p -2tÏ ªu CVdL ®ûN çiPûXùLôÓjÕd ùLôiúP CÚdÏm. CkRjRjÕYm Transformers Guß ùNôpXlTÓ¡\ ªuUôt±«p TVuTÓjRlTÓ¡\Õ.

CVdLj§u êXm çiPlThP ªuCVdÏ ®ûN EtTj§ ùNnRp (Production ofdynamically induced emf): GlùTôÝÕ JÚ LPj§LôkRl ×XjûR ùYhÓ¡\úRô AlùTôÝÕARtÏs CVdLj§u êXm çiPlThPªu CVdÏ ®ûN EtTj§ ùNnVlTÓ¡\Õ.AkR LPj§dLô] ªu ÑtßêPlTh¥ÚkRôp CkR CVdÏ ®ûN AkRªu Ñt±p ªuú]ôhPjûR ®û[®d¡\Õ.



130

CVdLj§u êXm çiPlThP ªu CVdÏ®ûNûV EtTj§ ùNnV úRûYVô]ûY

• LôkRl×Xm

• LPj§

• LôkRl×Xj§tÏm, LPj§dÏmCûPúVVô] E\Ü SLoÜLs

ùRôPo×ûPV LôkRl ×XjÕPu ‘V’ ùRôPo×§ûNúYLm Es[ LPj§ SLokRôp, AR]ôpçiPlTÓm ªu CVdÏ ®ûN ‘e’ Vô]Õ.

= BLV Sinθ úYôph BL CÚdÏm.

C§p

B = LôkRl×X APoj§ (ùPvXô - ®pA[®PlTÓ¡\Õ).

L = LôkRl×Xj§p LPj§dÏ úRûYVô]¿[m (ÁhP¬p).

V = LPj§dÏm LôkRl ×Xj§tÏmCûPúVVô] ùRôPo× §ûNúYLm (ÁhPo/ùNLi¥p).

θ = LôkRl ×XjûR LPj§ ùYhÓm úLôQm.

CkR U§l×Lû[ JÚ ¡Wôl Rô°p (graph sheet)T§®ÓYRu êXm, ºWô] LôkRl×Xj§p NUtßm S ÕÚYeLs ÑZÛm ùTôÝÕLPj§«u Esú[ HtTÓm ªu CVdÏ®ûN«u çiPp ûNu úYq Y¥®p (sinewave pattern) ©W§¨§jÕYlTh¥ÚlTûRLôQXôm.

CqYô\ô] ùNVpØû\«u A¥lTûP«pçiPlThP ªu CVdÏ ®ûNA¥lTûP«p UôßTÓm CVp©p CÚdÏm.úUÛm CkR AC ªuú]ôhPm DCªuú]ôhPUôL LmëúPhPôo (commutator)êXm DC ù_]úWhP¬p Uôt\lTÓ¡\Õ.

@©[mªe -u YXÕ ûL ®§ (Fleming’s righthand rule): CkR ®§«u êXm CVdLj§uêXm çiPlThP ªu CVdÏ ®ûN«u§ûN«û] AûPVô[m LôQXôm. TPm 6 -pLôh¥Ùs[ T¥ EeLs YXÕ ûL«p Es[LhûP ®Wp, Bs Lôh¥ ®Wp Utßm SÓ®Wp B¡VYtû\ JußdùLôuß 90°úLôQj§p CÚdÏUôß ûYjÕd ùLôs[Üm.C§p Bs Lôh¥ ®Wp LôkRl ×Xj§u§ûN«p CÚdÏm Utßm LhûP®Wp LPj§SLÚm §ûN«p CÚdÏm, G]úY SÓ ®WpçiPlThP ªu CVdÏ ®ûN §ûNûVdLôhÓm ARôYÕ TôoûYVô[ûW úSôd¡úVô(A ) TôoûYVô[¬PªÚkÕ ®X¡úVôLôi©dÏm.

CûRl úTôXúY, Ñtß YhPl TôûR«pEs[ ®ÓThÓs[ LPj§«u JqùYôÚ¨ûX«Ûm çiPlTÓm ªu CVdÏ®ûNûV LQd¡hÓ A±VXôm.



t¦uû] lqdÏ utßm a±®vp · ckr £ltjûr (imp) eÚyôdÏm ùnvttôh¥p ªlÜm £\ltôlÜm brkr...

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