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UNIQUE LEARNING CENTRE, ULLOOR, TVPM www.uniquetvm.com Physics Rotational motion & Gravitation Std: XI Marks: 200,Time: 1 hour 1. What is the maximum speed of a car taking a turn of radius 30 m on a level road if the coefficient of friction between the tyres and road is 0.4? (g = 9.8 ) A) 5.42 B) 6.27 10 C) 10.84 D) 21.68 E) 8.32 2. A curved road of radius is perfectly banked for a speed v. When a car of weight W goes round the curve with speed v (friction neglected), then the normal reaction of the road is N. Then: A) the centripetal force is resultant of W and N B) the normal reaction is W C) the centripetal force is zero D) the centripetal force is W E) None 3. A closed tube, partly filled with a liquid and set horizontal, is rotated about a vertical axis passing through its centre. In the process, the moment of inertia of the system about its axis would: A) increase always B) decrease always C) remain constant D) increase if tube is less than half filled , decrease otherwise E) cannot be predicted 4. Without weighing, how will you distinguish between the two identical balls of same material, but one being solid and the other one being hollow: A) by rolling them down an inclined plane in air B) by determining their moment of inertia about the centre C) by spinning them by equal torque D) all the above [E] none 5. Three identical rings, each of mass M and radius R are arranged as shown in figure. The moment of inertia of the arrangement about / is: [A] [B] [C] [D] [E] 6 .A flywheel of momentum of inertia 0.5 kg is brought to rest in 10 second by a constant couple of 10 N m acting along on the flywheel. What was the initial angular velocity of the flywheel in radians [A] 0.5 [B] 2 [C] 60 [D] 100 [E] 200 7. A cubical block of side L rests on rough horizontal surface with coefficient of friction. A horizontal force F is applied on the block as shown in figure. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is: [A] Infinitesimal [B] [C] [D] mg(1 – ) [E] √3 1 8. In the circular motion (figure) speed of the particle is increasing. The direction of the angular acceleration vector is: [A] Opposite to that of angular velocity vector [B] ‘’going in’’. The plane of the figure [C]’’coming out of ’’ the plane of the figure [D] same as that of the angular velocity vector [E] Both B and D 9. If the change in value of g at a height h above the surface of the earth is the same as the change in value at a depth x below it. Then: [A] x = h [B] x=2h [C] 2x = h [D] = h [E]X = 10. The height from the surface of the earth at which the intensity of gravity become g/2 is approximately: [A] 2650 km [B] 5400km [C] 1600km [D] 3200km [E] 6400km

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Page 1: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

UNIQUE LEARNING CENTRE, ULLOOR, TVPM www.uniquetvm.com Physics Rotational motion & Gravitation Std: XI Marks: 200,Time: 1 hour 1. What is the maximum speed of a car taking a turn of radius 30 m on a level road if the coefficient of friction between the tyres and road is 0.4? (g = 9.8����) A) 5.42 ���� B) 6.27 �10���� C) 10.84 ���� D) 21.68���� E) 8.32 ����

2. A curved road of radius � is perfectly banked for a speed v. When a car of weight W goes round the curve with speed v (friction neglected), then the normal reaction of the road is N. Then: A) the centripetal force is resultant of W and N B) the normal reaction is W C) the centripetal force is zero D) the centripetal force is W E) None

3. A closed tube, partly filled with a liquid and set horizontal, is rotated about a vertical axis passing through its centre. In the process, the moment of inertia of the system about its axis would: A) increase always B) decrease always C) remain constant D) increase if tube is less than half filled , decrease otherwise E) cannot be predicted

4. Without weighing, how will you distinguish between the two identical balls of same material, but one being solid and the other one being hollow: A) by rolling them down an inclined plane in air B) by determining their moment of inertia about the centre C) by spinning them by equal torque D) all the above [E] none

5. Three identical rings, each of mass M and radius R are arranged as shown in figure. The moment of inertia of the arrangement about��/ is:

[A] �� ��� [B] ��� [C] �

� ��� [D] �

� ��� [E] �

� ���

6 .A flywheel of momentum of inertia 0.5 kg �� is brought to rest in 10 second by a constant couple of 10 N m acting along on the flywheel. What was the initial angular velocity of the flywheel in radians ��� [A] 0.5 [B] 2 [C] 60 [D] 100 [E] 200

7. A cubical block of side L rests on rough horizontal surface with coefficient of friction�. A horizontal force F is applied on the block as shown in figure. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is:

[A] Infinitesimal [B] ���

[C]���

[D] mg(1 – �) [E] �√3 � 1�� ���

8. In the circular motion (figure) speed of the particle is increasing. The direction of the angular acceleration vector is:

[A] Opposite to that of angular velocity vector [B] ‘’going in’’. The plane of the figure [C]’’coming out of ’’ the plane of the figure [D] same as that of the angular velocity vector [E] Both B and D

9. If the change in value of g at a height h above the surface of the earth is the same as the change in value at a depth x below it. Then: [A] x = h [B] x=2h [C] 2x = h [D] ��= h [E]X = ��

10. The height from the surface of the earth at which the intensity of gravity become g/2 is approximately: [A] 2650 km [B] 5400km [C] 1600km [D] 3200km [E] 6400km

Page 2: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

11. When the masses of two bodies and the distance between them are doubled, the gravitational force is: [A] halved [B] doubled [C] made 4 times [D] made ¼ times [E] the same

12. Two satellite A and B of same mass are moving in circular orbits around the earth so that B is in outer orbit. Then: [A] A has greater kinetic energy and total energy is the same [B] A has greater potential energy and total energy is different for A and B [C] A has smaller p.e and total energy is the same [D]A has greater kinetic energy and smaller total energy than B [E] A and B having the same p.e. and k.e.

13.������� denote the escape velocities from the Earth and another planet having twice the radius and the same mean density as the Earth. Then:

[A] �� = �� [B] �� = ��

� [C] �� = 2 ��

[D] �� = ��

� [E] �� =

��

√�

14. The weight of the body at earth’s surface is W. At a depth halfway to the centre of the earth it will be: [A] W [B]W/2 [C] W/4 [D] W/8 [E] Zero

15. In a gravitational field , at a point where the gravitational potential is zero: [A] gravitational field must be zero [B] gravitational field need not be zero [C] gravitational field is infinity [D] gravitational field is a constant [E] gravitational field is independent of potential

16. Keplers II law is: [A] total acceleration is zero [B] tangential acceleration is zero [C] radial acceleration is zero [D] areal velocity is constant [E] square of the period is proportional to cube of the distance of the planet from the sun

17. The gravitational force of attractions between two bodies, each of mass 1 kg and separated by 1 m, is : [A] 6.675 �10���� [B] 6.675 �10��� [C] 6.675 N [D] 1N [E] none

18. A satellite of mass m is circulating around the Earth with constant angular velocity. If radius of the orbit is �� and mass of the Earth M, the angular momentum about the centre of the Earth is :

[A] m ����� [B] M�����

[C] m �����

[D] M �����

[E] Mm���

19. A body weight 700 g wt. on the surface of the Earth. How much will it weight on the surface of a planet whose mass is 1/7 and radius is half that of the Earth: [A] 100 g wt [B] 400 g wt [C] 50 g wt [D] 300g wt [E]200 g wt

20. If the earth is treated as a sphere of radius R and mass M, its angular momentum about the axis of its diurnal rotation with period � is :

[A] �����

�� [B]�����

�� [C] ��

����

[D] ����

� [E] ����

��

21. Two planets have radii in the ratio x: y and density in the ratio m: n. The acceleration due to gravity ‘g’ is in the ratio : [A] nx:ny [B] ny:mx [C] mx : ny [D] my : nx [E] �� x : �� y

22. Three masses each equal to M, are placed at the three corners of a square of side a. The force of attraction on unit mass at the fourth corner will be :

[A] �����

[B] ����√3 [C] ���

��

[D] ����

����√2� [E] ��

�� � �√�� √2�

23. The ratio of the kinetic energy required to be given to a satellite so that escape the gravitational field of earth to the kinetic energy required to put the satellite in a circular orbit just above the free surface of earth is : [A] 1 [B] 2 [C] 3 [D] 9 [E] 0.5

24. The period of Moon’s rotation round the earth is nearly 29 days. If Moon’s mass were 2 fold its present value, and all other things remain unchanged, the period of Moon’s rotation would be nearly: [A] 29 √2 days [B] 29/ √2 days [C] 29 �2days [D] 29 days [E] 29/ √3 days

25. The ratio of the acceleration due to gravity on two planets ������� is ��. The ratio of their respective radii is �� . The ratio of their respective escape velocities is :

[A] ����� [B] �2���� [C] �����

[D] �����

[E] none

26. Dimensional formula for gravitational constant:: [A] �������� [B] ������� [C] ML��� [D] ������ [E] ������

Page 3: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

27. An iron balls and a wooden ball of the same radius are released from a height in vacuum. The relation between time taken by iron ball (��� and wooden ball���) is:

[A] �� = �� [B] �� > �� [C] ��>�� [D] ��~�� [E] �� >> ��

28. Two satellite are revolving around earth in circular orbits radii twice and four times of earth. If the ratio of their masses is 2:3 , then ratio of their total energy is …………… [A] 2:1 [B] 1:2 [C] 3:4 [D] 4:3 [E] 1:1

29. A smooth tunnel is drilled through the center of earth. A body is dropped into the tunnel from one end . When it reaches the centre of earth: [A] velocity is minimum [B] velocity is maximum and acceleration is minimum [C] velocity and acceleration, both are maximum [D] velocity is zero and acceleration is zero [E] velocity is maximum and acceleration is zero

30. For satellite moving in circular orbit around a planet, kinetic energy E and time period T are related by : [A] E ∝ T [B] E ∝ �� [C] E ∝ ��/� [D] E ∝ ��/� [E] E ∝ ���/�

31. Escape velocity from the solar system is : [A] 11.2 km/s [B] 42 km/s [C] 12km/s [D] 2.4 km/s [E] 30km/s

32. Escape velocity from the sun: [A] 11.2 km/s [B] 42 km/s [C] 12km/s [D] 2.4 km/s [E] 618km/s

33. Relation between gravitational potential (u) and gravitational field (E) is : [A] E= u/r [B] u= dE/dr [C] u = -dE/dr [D] E = -du/dr [E] E = du/dr

34. The mass of a planet is 6 times that of Earth. The radius of planet is twice that of earth. If the escape velocity from earth is v, then the escape velocity from the planet is : [A] √3 � [B] √2 � [C] � [D] √5 � [E] 2�

35. If the earth is at 1/4th of its percent distance from the sum , the duration of the year will be : [A]the same as now [B] half of the present year [C] one – fourth present year [D]one – eighth present year [E] 1/64th of present year

36. The gravitational potential energy of a rocket of mass 100Kg at a distance 10�m from the earth’s centre is 4 � 10�Joules. The weight of the rocket in Newton’s at a distance 10�m from the earth is : [A] 980N [B] 4 � 10��N [C] 4N [D] 100 N [E] 400N

37. For identical point masses each equal to m are placed at the corners of a square of side a. The force on a point mass m place at the point of intersection of the two diagonals is:

[A] ����/

�� [B] ���

�� [C] ����

�� [D] ����/

�� [E] Zero

38. An infinite number of identical point masses each equal to m are placed at X = 1 , X = 2 , X= 4 , X=8….. The total gravitational potential at point X = 0 is : [A] –Gm [B] -2Gm [ C] 2Gm [D] Zero [E] Infinite

39. An earth satellite can revolve around the Earth only in such an orbit whose plane coincides with: [A] the plane of same latitude circle of Earth [B] a vertical plan not containing the centre of Earth [C] the plane of tropic of cancer [D] the plane of any great circle around the Earth [E] none

40. The gravitational force of attraction between a uniform sphere of mass M and a uniform rod of length � and mass m oriented as shown is:

[A] ���������

[B] ����

[C] ����� � ��

[D] ��� � ��mMG [E] none

41. A coin is placed on a gramophone record rotating at a speed of 45 rpm . It flies away when the rotational speed is 50rpm. If two such coins are placed one over the other on same record , both them will fly away when the rotational speed is : A)12.5 rpm B) 25 rpm C) 50 rpm D) 100 rpm E) 10 rpm

42. Three particles of masses 1 kg, 2kg and 3kg are placed at the corners of an equilateral triangle of side 1m.The co-ordinates of the centre of mass with respect to 0:

A) ��� , √�

�� B) � �

�� , √�

��

C) �√��, √�

�� D) � �

�� , √���� E) ��

� , ���

43. A shell at rest explodes; the centre of mass of the fragment:

Page 4: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

A) Moves along a parabolic curve B) Moves along an elliptical path C) Moves along a straight line D) Remains at rest E) Moves along any direction

44. Four cubes of side ‘a’ each of mass 40g , 20g, 10g and 20g are arranged in the X-Y plane as shown in figure . The co- ordinates of the centre of mass of the combination with respect to 0:

A) ����

a,����� B) ��

�� a,��

��� C) ��

�� a,��

�� a

D)����

a,����� E)��

���, �

���

45. The distance between the centres of carbon and oxygen atoms in the carbon monoxide gas molecule is 1.2 � 10��cm. The centre of mass of the molecule with respect to the carbon atom is: A) 0.69 � 10��Cm B) 1.2 � 10�� cm C) 0.6 � 10���Cm D) 0.6 � 10��Cm [E] 0.4 � 10���Cm

46. A force of 16 N is used to rotate a circular wheel of diameter 50cm from rest about its axis. If there is no friction and the angular acceleration produced is 2rad/��the moment of inertia of the wheel about the axis is: A) 16 kg �� B) 5 kg �� C) 2 kg �� D) 8 kg �� E) 4 kg ��

47. A particle of mass ‘m’ describing a circular path of radius ‘r’ with uniform speed. If L is the angular moment of the particle about the axis of the circle the kinetic energy of the particle is :

A) ��

� B) ����

C) ��

���� D) �

��� �

E) ��

���

48. A circular ring of mass M and radius � is rotating about its axis with constant angular velocity �. Two object each of mass ‘m’ are attached gently to the opposite ends of a diameter of the ring. The wheel now rotates with angular velocity:

A) �����

B) �������������

C) ������

D) � �������

49. A circular disc of radius x has uniform thickness. A circular hole of diameter equal to the radius of the disc has been cut out as shown. The centre of gravity of the remaining part of the disc lies on the diameter of disc at a distance to the left of the centre of the original disc:

A) X B) ��

C) �� D) �

� E) �

��

50. A motor cyclist is moving on a circular track of radius 80m with a velocity of 72 Km/hr . He has to lean from the vertical approximately through an angle: A) ����� (1/4) B) ����� (1/2) C) ����� (1/3) D) ����� (2) E) ����� (3)

Page 5: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

(Online test) Rotational motion & Gravitation - Answer key

1. C 2. A

3. A 4. D

5. D

6. E

7. C

8. E 9. B

10. A

11. E

12. D

13. B

14. B

15. B

16. D

17. A

18. A

19. B

20. A

21. C 22. D

23. B 24. D 25. A

26. A

27. A

28. D

Page 6: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

29. E

30. E

31. B

32. E

33. D

34. A

35. D

36. C

37. E

38. B

39. D

40. A

41. C

42. B

43. D

44. C

45. A

46. C

47. C

48. C

49. D

50. B

Page 7: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

Answer key and explanation

1. C V = √0.4 � 9.8 � 30 ����; = √117.6 ���� = 10.84 ���� 2. A

The angle between N and W is 180 – �. Also , N sin � provides the necessary centripetal force .

Resultant of N and W = ��� ��� � 2������180� ��

= √�� �������� � 2������� = ����1 ������� = N sin� 3. A Centripetal force drives liquid outward thereby increasing moment of inertia 4. D

The hollow ball shall have larger moment of inertia because of ‘farther distribution of mass 5. D Moments of inertia of rings I and II about

��/ = 2 � �� ��� = 3 ���

Moment of inertia of ring III about ��/ = �� ���

Total moment of inertia = 3 ��� + �� ��� = �

� ���

6. E � =� ∝ , � = ���

� , t = ���

� ; or

�� = ���

= ������.�

� 200������

7. C Clearly , the block shall topple about its edge through O . The torque FL of the applied force is clockwise.

The torque ����

of the weight is antilock wise.

8. [ E ] ��� = ���� � ����� = ∝��� ��� 9. B

g �1 ������ = g �1 � �

��� ie , X = 2h

10. A �/ = �

������� . �/ = �

11. E 12. D

13. B

V = �����

or V = ����� �

�����

or V = �������� or V = R ��

���� ,

now �� ∝ ������ ∝ 2� or ��

�� = 2 or �� = ��

14. B

Page 8: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

15. B 16. D

17. A

F = �������

; �� = �� = 1 kg ; r = 1m

∴ F = G

18. A

L = ����� ; L = m �������� ; L = m �����

19. B

�/ = G . ������

��� = �

� ����

= ���

�/ = ��/ = m ����� = �

� mg = �

� � 700 � 400�.��.

20. A Angular momentum = ��.

= ����� � ��

�� ���

��

21. C

g = ������ ; ∴ ��

�� = ����

�� �� = ��

��

22. [D]

�� � �� = ����

Resultant of ������� is √2 ����

�� = ���√����

= �����

Now √�����

and �����

act in the same direction. Their resultant is √�����

+ �����

or ����

�√2 ����

23. B �� = �2�� when orbit is close to earth,

�� = ��� ; �� = �� ���� = �

� m � 2�� � ���;

�� = �� ���� = �

� mgR ;

∴ �����/�����

= 2

24. D The period of rotation does not depend upon mass of the satellite. 25. A ����

= �����������

= �����

26. A

27. A

Same force acts on both

28. D

Page 9: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

Total energy E = ������

�� =��������

�� =��������

�� ��

= ����

� ����

= �� � ���

��� = �

29. E

30. E

E = �� ��� = ���

��

ie E ∝ �� �� ∝ �� or r ∝ ��/� or E ∝ �

��/�

31. B

32. E

33. D

34. A

�� = �������

= ���������

= �3 ������ = √3 v

35. D

�� = T �� = ? �� = r �� = ��

����

= �������/�

�� = �� �������/�

= T � �����/�

= �� T

36. C

g’ = ����

P.E = ����

= 4� 10� ∴ ���

= �����

g’ = �����

�� = 4 �10�� �� = = 4 �10� �100N

37. E

38. B

V = - Gm���� �

�� �

��⋯ � - Gm[1 + 1] = - 2Gm;

��� �

���

� + ………. ∞ = 1

39. D

40. A

Mass per unit length = ��

mass of section of length dx = ��

dx

Page 10: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

�� = �� ��� ���

��

F= � ������

���� �x = ���

� � �

������ ��

= ����

� x������� �� = ���

� ��

����

������

��� = ���

� ��������� = - ���

� �����

��� = ���

������

41. C

Coin fly away when ��� R = � X mg : � is independent of mass ∴ 50 rpm

42. B

��� = �� ���������� ����������

= �����������.������

= ����

��� = ��������� �������������

���������√��

����� = √�

� ∴ co – ordinate � �

�� , √�

��

43. D

44. C

X = �����������

�������

��� ����

���

��� = ���

��

Y = ����������� �����

�����

��

��� = ���

��

Co- ordinate of C.M = ������, ��

����

45. A If X be the X- coordinate of the centre of mass then

X= ������ ��.������

����� = 0.69 �10��

46. C

� = ∝ ; � = � � � � 16 � 0.25 = 4 Nm;

� = �∝

= �� = 2 kg ��

47. C

I = m�� ; E = ��

��� ��

����

48. C

��� � = (��� + 2 m��) �� ; ∴ ������

� �/

49. D

Mass per unit area = ; Mass = ����;

mass removed = � ��

��

Page 11: UNIQUE LEARNING CENTRE,exam.uniquetvm.com/download/QAE/OE2016-17-10.pdf · UNIQUE LEARNING CENTRE, ULLOOR, ... areal velocity is constant [E] ... Dimensional formula for gravitational

Mass remaining = ���� - � ��

�� = �

� � �

�� ;

�� ����� = � �

�� . �

� ; ∴ r = �

50. B

tan � � ��

�� = ���

����� � �

� ; � � ����� ��

��