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