MEASUREMENT, PHYSICAL MEASUREMENT, CONVERSION OF FOUND OFF, FLOATING POINT MEASUREMENT, DIMENSIONS, UNITS, BASIC FORMULAE

1. Nature Of The Physical World
And Measurement

2. 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

3. Length
t Mass
Time
Electric current
Fundamental
Quantity Temperature
Luminous
Intensity
Physical Quantity Amount of
substance
Plane angle
Solid angle
Derived Quantity Area, Volume,
Density

4. S.NO POWER PREFIX ABBREVIATION
OF TEN
1 10-15 Femto f
2 10-12 Pico p
Expressin 3
4
10-9
10-6
Nano
Micro
n
μ
g Larger 5 10-3 Milli m
And 6
7
10-2
10-1
Centi
Deci
c
d
Smaller 8 101 Deca da
Physical 9
10
102
103
Hecto
Kilo
h
k
Quantities 11 106 Mege M
12 109 Giga G
13 1012 Tera T
14 1015 peta P

5. LIGHT YEAR AND ASTRONOMICAL UNIT
 Light Year
It is the distance travelled by light in one
year in vaccum.
1 Light Year = 9.467 x 1015m
 Astronomical 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

6.  Determinationof Distance
Laser pulse method
 Determination of mass
 Determinationof time
Atomic clocks – 1013 sec
Quartz clocks – 109 sec

7. 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

8. 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.

9. 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.

10. Rounding Off Examples
 53.473 kg – 53.6 kg
 0.575 m – 0.58 m
 0.495 – 0.50

11. 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.

12. Dimensional Analysis
Dimensions of a physical quantity are the powers to which the
fundamental quantities must be raised.
Fundamental Quantity Dimension
Length L
Mass M
Time T
Temperature K
Electric current A
Luminous intensity cd
Amount of substance mol

13.  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.

14. 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.

15. 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.