9011041155 / 9011031155

1

Measurements

Physics

Physics is a branch of science which deals with study

of natural phenomenon of non-living things.

Origin “fuses”

Physical quantities

The quantities which can be measured with physical

apparatus or physical means are called physical

quantities.

e.g.mass Length

9011041155 / 9011031155

2

Time Temperature

etc.

Physical quantities are expressed in terms of

magnitude and unit.

Non – physical quantities

The quantities which cannot be measured with physical

apparatus or no physical apparatus is available for their

measurement are called non-physical quantities.

e.g. Intelligence of a person, happiness etc.

9011041155 / 9011031155

3

Measurement

Measurement of a physical quantity is its careful and

accurate comparison with the standard of that quantity.

Unit

The standard used for comparison of a physical

quantity is called unit of that quantity.

e.g. 1kg

9011041155 / 9011031155

4

Magnitude

Magnitude of a physical quantity is the number which

indicates how many times the unit is contained in it.

e.g. 10 litres

The physical quantities are classified in to two

types

1. Fundamental quantities :- The physical quantities

which can be independently measured and

expressed are called fundamental quantities. Thus,

these quantities can be measured and expressed

without taking help of other quantities.

e.g. length, mass, time, temperature etc.

Fundamental units :- The units of the fundamental

quantities are called fundamental units.

9011041155 / 9011031155

5

e.g. metre, kilogram, second etc.

Fundamental quantities

i. length Metre (m)

ii. mass Kilogram (kg)

iii. time Seconds (s)

iv. temperature Kelvin (K)

v. Electric current Ampere (A)

vi. Luminous

Intensity

Candela (cd)

viii. Amount of

substance

Mole (mol)

Supplementary Quantities

i. Plane angle → Radian → rad

ii. Solid Angle → Steradian → sr

9011041155 / 9011031155

6

iii. Frequency → 1/t = 1/s = Hertz (Hz)

2. Derived quantities :- The physical quantities which

require two or more fundamental quantities for their

measurement and expression are called derived

quantities.

e.g. speed, acceleration, force etc.

Derived units :- The units of derived quantities are

called derived units.

e.g. m/s, m/s2, newton etc.

Requirements of good units

1. The unit should be easy to use and read.

2. Its magnitude should not change with respect to

time, temperature, place and observer.

3. It should be easily reproducible. It means, it should

be easy to copy and can be produced anywhere

any quantity.

4. It should be acceptable worldwide.

9011041155 / 9011031155

7

(universally acceptable )

System of units

The fundamental units together with all derived units

form a system of units. Formerly there were different

unit systems used in different countries. Some of the

most common unit systems were as follows :-

1. C.G.S.

2. M.K.S.

3. F.P.S.

4. S.I.( System International ) :- To avoid difficulties

in inter conversions of units and to have uniformity

in the units used all over the world, General

Conference of weights and Measures suggested an

improved metric system called System International

in 1960. It was accepted by I.S.O.( International

Standards Organization ) in 1962. This includes all

the fundamental units from M.K.S. and over 450

9011041155 / 9011031155

8

derived units. As far as possible the units are

named after renowned scientists to honour them.

Before the introduction of S.I. exchange of

information between the scientists of different

countries was difficult because of the difference

between the unit systems used by them. With the

worldwide use of S.I. this difficulty is removed.

Now in this common language of units, scientists

engineers and technicians all over the world can

exchange their ideas, criticism easily. So, this

system has bridged-up the gap between them.

Rules of writing S.I. units

1. metre, joule, newton

Metre, Joule,Newton

9011041155 / 9011031155

9

2. cm, m/s, J, N

Cm, M/s, j, n etc.

3. singular form only. plural form of units:- not allowed,

e.g. While speaking, we may say that the mass is

100 kilograms,

but while writing, we should write 10kg only and

not 10kgs.

4. No punctuation marks

e.g. the unit newton metre should be written as Nm

and not like N-m or N,m etc. m/s is a valid unit

because the slash (/) is not a punctuation mark. It is

a mathematical operator.

9011041155 / 9011031155

10

Dimensions

Increasing the power of fundamental units to find out

units of derived quantities is known as dimensions.

1.

0 1 1

displacementVelocity

Time

VT

[ M L T ] m / s

l

2. Area = ℓ2

= [ M0 L

2 T

0] = m

2

3. Volume = ℓ3

= [ M

0L

3T

0] = m

3

9011041155 / 9011031155

11

4.

2

0 1 2 2

V / TAcceleration

T T

T

M LT m / s

l

l

5. Force = ma

= m × ℓ / T2

= [ M1L

1T

-2] = kg m / s

2 = N

6. Work = F . ℓ

= ma . ℓ

= m . ℓ / T2 . ℓ

= m . ℓ2 / T2

= [ M1 L

2 T

-2] = kg . m / s

2 = J

9011041155 / 9011031155

12

7.

2

2

2 2

1 1 2 2

ForcePr essure

Area

ma

m. / T m

.T

M L T kg m / s

l

l

l l

8.

2

21 2 3 2 3

3

WorkPower

Time

F .

T

ma .

T

m . / T .

T

mM L T kgm / s w

T

l

l

l l

l

9011041155 / 9011031155

13

9. P.E = mgh

2

1 2 2 2 2

m. / T .

M L T kgm / s J

l l

10.

2

2 2

1 2 2 2 2

1K.E mv

2

1m. / t

2

[M L T ] kgm / s J

l

11. Impulse = F.T

= ma . T

= m . ℓ / T2 . T

2

1 1 1

m. . T

T

MLT kg m / s Ns

l

9011041155 / 9011031155

14

12. Momentum = mv

= m . ℓ / T

= [ M1 L

1T

-1 ]

= kg m / s

13.

3

1 3 0 3

massDensity

Volume

m

M L T kg/m

l

M = [ M1L

0T

0]

ℓ = [ M0L

1T

0]

T = [ M0L

0T

1]

9011041155 / 9011031155

15

Uses of dimensional analysis

1. To check correctness of equation.

principle of homogeneity:- It states that dimensions

towards both sides of equation for each term are

same. Then the given equation is dimensionally

correct.

For e.g.

1. 21s ut at

2

s is displacement

u = initial velocity

t = time

a = acceleration

L.H.S = ∴ S = [ M0L

0T

1] ….. (1)

R.H.S

9011041155 / 9011031155

16

∴ ut = [ M0L

1T

-1] [ M

0L

0T

1]

= [ M0L

1+0T

-1+1]

= [ M0L

1T

0] …… (2)

21at

2 = [ M

0L

1T

-2] [ M

0L

0T

1]2

= [ M0L

1T

-2] [ M

0L

0T

2]

= [ M0L

1T

0] …….. (3)

From (1), (2) & (3) we can say that the given

equation is dimensionally correct.

2. v2 = u

2 + 2as

3. v = u + at

4. w = w0 + mc2

w = work

w0 = work

m = mass

c = speed of light

9011041155 / 9011031155

17

2. To find out conversion factor in between different

units of same quantity .

e.g.1 Let MKS unit of force if Newton (N)

CGS unit of force is Dyne

Let 1 N = x dyne

Substituting dimensions of force in above

equation,

1 1 2 1 1 2

1 1 1

1 1 2

1 1 1

1 1 2

2

M L T x M LT

M L Tx

M LT

kg m s

2g cm s

3 2

3 2

5

5

10 10 cmg

g cm

10 10

x 10

1N 10 dyne

1 J = x erg

9011041155 / 9011031155

18

e.g.2

v = u + at

v = final velocity

u = initial velocity

a = acceleration

t = time

L.H.S = v

∴ v = [ M0L

1T

-1] ……… (1)

R.H.S = u

∴ u = [ M0L

1T

-1] ……… (2)

R.H.S at = [ M0L

1T

-2] [ M

0L

0T

1]

= [ M0L

1T

-1] ………… (3)

From (1), (2), (3) we can say that the given

equation is dimensionally correct.

9011041155 / 9011031155

19

e.g. 3

v2 = u

2 + 2as

v = final velocity

u = initial velocity

a = acceleration

s = displacement

L.H.S = v2

∴ v2 = [ M

0L

1T

-1]2

= [ M0L

1T

-1] …….. (1)

R.H.S = u2

∴ u2 = [ M0L

1T

-1]

2

= [ M0L

2T

-2] …….. (2)

as = [ M0L

1T

-2] [ M

0L

1T

0]

= [ M0L

1+1 T

-2+0]

= [ M0L

2T

-2] …….. (3)

9011041155 / 9011031155

20

From (1), (2), & (3) we can say that the given

equation is dimensionally correct.

e.g.4

w = w0 + mc2

w = work

w0 = work

m = mass

c = speed of light

L.H.S = w

∴ w = [ M1L

2T

-2] ……… (1)

R.H.S = w0 + mc2

w0 = [ M

1L

2T

-2] ……… (2)

mc2 = [ M

1L

0T

0] [ M

0L

1T

-1]2 = [M

1L

0T

0] [M

0L

2T

-2]

= [M1L

0+2 T

0-2] = [M

1L

2T

-2]

From (1), (2), & (3) we can say that the given

equation is dimensionally correct.

9011041155 / 9011031155

21

1 J = x erg

Substituting dimensions of energy in above

equation

1 2 2 1 2 2

1 1 1

1 2 2

1 1 1

1 2 2

2 2

M L T x M L T

M L Tx

M L T

kg m secx

2 2g cm sec

2

23 10 cm10g

g

cm

∴ x = 103 × 10

4 ∴ x = 107

∴ 1 J = 107 erg

9011041155 / 9011031155

22

• Ask Your Doubts

• For inquiry and registration, call 9011041155

/ 9011031155.