5. DIMENSIONAL FORMULAR

1.5 DIMENSIONAL FORMULAE

Dimensional Formula: An expression along with the power of mass, length & time which indicates how physical quantity depends upon fundamental physical quantity.

e.g.          Speed = Distance/Time

= [L1]/[T1] =[M0L1T-1]

It tells us that speed depends upon L & T. It does not depend upon M.

1.5.1 Dimensional Equation: An equation obtained by equating the physical quantity with its dimensional formula is called a dimensional equation.

The dimensional equation of area, density & velocity are given as under- Area = [M0L2T0]

Density = [M1L-3T0] Velocity = [M0L1T-1]

Dimensional formula SI& CGS unit of Physical Quantities

 

Sr.

No.

Physical Quantity

Formula

Dimensions

Name of S.I unit

1

Force

Mass × acceleration

[M1L1T-2]

Newton (N)

2

Work

Force × distance

[M1L2T-2]

Joule (J)

3

Power

Work / time

[M1L2T-3]

Watt (W)

4

Energy ( all form )

Stored work

[M1L2T-2]

Joule (J)

5

Pressure, Stress

Force/area

[M1L-1T-2]

Nm-2

6

Momentum

Mass × velocity

[M1L1T-1]

Kgms-1

7

Moment of force

Force × distance

[M1L2T-2]

Nm

8

Impulse

Force × time

[M1L1T-1]

Ns

9

Strain

Change in dimension

/ Original dimension

[M0L0T0]

No unit

10

Modulus of

Elasticity

Stress / Strain

[M1L-1T-2]

Nm-2

11

Surface energy

Energy / Area

[M1L0T-2]

Joule/m2

12

Surface Tension

Force / Length

[M1L0T-2]

N/m

13

Co-efficient of

Viscosity

Force × Distance/

Area × Velocity

[M1L-1T-1]

N/m2

14

Moment of inertia

Mass  ×  (radius  of

gyration)2

[M1L2T0]

Kg-m2

15

Angular Velocity

Angle / time

[M0L0T-1]

Rad.per sec

16

Frequency

1/Time period

[M0L0T-1]

Hertz

17

Area

Length × Breadth

[M0L2T0]

Metre2

18

Volume

Length × breadth ×

height

[M0L3T0]

Metre3

19

Density

Mass/ volume

[M1L-3T0]

Kg/m3

20

Speed or velocity

Distance/ time

[M0L1T-1]

m/s

21

Acceleration

Velocity/time

[M0L1T-2]

m/s2

22

Pressure

Force/area

[M1L-1T-2]

N/m2


Assignment

Instructions: This Assignment is to be done and submitted on or before 13th October, 2025.

1.  Into how many categories is physical quantity classified based on dimensional analysis, explain? 

2. Derive the dimensional formula of following Quantity & write down their dimensions.

(i)   Density  

(ii) Power

(iii) Co-efficient of viscosity  

(iv) Angle

3. Explain which of the following pair of physical quantities have the same dimension:

 (i) Work &Power (ii) Stress & Pressure (iii) Momentum &Impulse