Nature Of The Physical World And Measurement

Forces of Nature

Sir Issac Newton,“Force is the external agency applied on a

body to change its state of rest and motion”◦Gravitational force◦Electromagnetic force◦Strong nuclear force◦Weak nuclear force

t

Physical Quantity

Fundamental Quantity

Length

Mass

Time

Electric current

Temperature

Luminous Intensity

Amount of substance

Plane angle

Solid angle

Derived Quantity

Area, Volume, Density

Expressing Larger And Smaller Physical Quantities

S.NO POWER OF TEN

PREFIX ABBREVIATION

1 10-15 Femto f

2 10-12 Pico p

3 10-9 Nano n

4 10-6 Micro μ

5 10-3 Milli m

6 10-2 Centi c

7 10-1 Deci d

8 101 Deca da

9 102 Hecto h

10 103 Kilo k

11 106 Mege M

12 109 Giga G

13 1012 Tera T

14 1015 peta P

Light YearIt is the distance travelled by light

in one year in vaccum. 1 Light Year = 9.467 x 1015mAstronomical unit

It is the mean distance of the centre of the sun from the centre of the Earth.

1 Astronomical Unit (AU) = 1.496 X 1011m

LIGHT YEAR AND ASTRONOMICAL UNIT

Determination of DistanceLaser pulse method

Determination of mass

Determination of timeAtomic clocks – 1013 secQuartz clocks – 109 sec

Significant figures

The number of meaning digits in a number is called the number of significant figures.

RULES

1. All the non- zero digits in a number are significant.

2. All the zeros between two non-zeros digits are significant, irrespective of the decimal point.

3. The zeros at the end without a decimal point are not significant.

4. The trailing zeros in a number with a decimal point are significant

Significant Figures Examples

0.0631 – Three Significant Figures. 56700 - Three Significant Figures.0.00123 – Three Significant Figures.30.00 – Four Significant Figures. 6.320 – Four Significant Figures. 600900 – Four Significant Figures.346.56 – Five Significant Figures 5212.0 – Five Significant Figures.

Rounding Off

If the insignificant digit is more than 5,◦The preceding digit is raised by 1.

If the insignificant digit is not more than 5,◦There is no change.

If the insignificant digit is 5◦Even

there is no change.◦Odd

The preceding digit is raised by 1.

Rounding Off Examples

53.473 kg – 53.6 kg

0.575 m – 0.58 m

0.495 – 0.50

Errors in Measurement♣ Constant Errors

It is due to faulty calibration of the scale in the measuring instrument.

♣ Systematic Errors

These are errors which occur due to a certain pattern or system.♣ Gross Errors

a. Improper setting of the instrument.

b. Wrong recording of the observation.

c. Not taking into account sources of error and precautions.

d. Usage of wrong values I the calculation.♣ Random Errors

It is very common that repeated measurement of a quantitative values which are slightly different from each other.

Dimensional Analysis

Fundamental Quantity

Dimension

Length L

Mass M

Time T

Temperature K

Electric current A

Luminous intensity cd

Amount of substance mol

Dimensions of a physical quantity are the powers to which the fundamental quantities must be raised.

Dimensional Quantities◦ Dimensional variables are those physical quantities which

possess dimensions but do not have a fixed value.

Ex. Velocity, force, etc.,

Dimensionless Quantities◦ There are certain quantities which do not possess dimension .

Ex. Strain, angle, specific gravity, etc.,

Principle of homogeneity of dimensions◦ An equation is dimensionally correct if the dimensions of the

various terms on either side of the equation are the same.

Ex. A+ B = C is valid only if the dimensions of A, B & C are the same.

Uses of Dimensional Analysis

Convert a physical quantity from one system of units to another.

Check the dimensional correctness of a given equation.

Establish a relationship between different physical quantities in an equation.

Limitations of Dimensional Analysis

The value of dimensionless constants cannot be determined by this method.

This method cannot be applied to equations involving exponential and trigonometric functions.

It cannot be applied to an equation involving more than three physical quantities.

It can check only whether a physical relation is dimensionally correct or not. It cannot tell whether the relation is absolutely correct or not.