# Dimensional Formula: Pressure, Power, Kinetic Energy, and Density

Solved Example 6

The dimensional formula of the pressure is…..

a) ML2T-2 b) ML-1T-2 c) a or b d) MLT

Steps:

pressure = ForceArea = MLT-2L2

= ML-2T-2

= ML-1T-2

-unit → kg.m-1.s-2= kg./s2= N/m2= N.m-2= J/m3= J.m-3

Solved Example 7

The dimensional formula of the work (energy) is ….

a) ML2T-2 b) MLT-2 c) a or b d) MLT

Steps:

(Energy) Work = Force × displacement

W = F × d

= ML2T-2 × L

= ML2T-2

- unit → kg.m2. s-2 = kg . m2/s2 = Joule = N.m

Note: – Any number has no dimension (as: π ,2,12 ,….)

Solved Example 8

The dimensional formula of kinetic energy is….

a) ML2T-2 b) ML2T-3 c) a or b d) MLT

Steps:

K.E = 12 m v2

= M (LT-1)2

= ML2T-2

- unit → kg.m2. s-2 = kg . m2/s2 = Joule = N.m

Solved Example 9

The dimensional formula of the power is….

a) ML2T-1 b) ML2T-3 c) a or b d) MLT

Steps:

Power = worktime = ML2T-2 T

= ML2T-2T-1

= ML2T-3

- unit → kg.m2. s-3 = kg . m2/s3 = Js = J.s-1 = N.m/s = N.m.s-1

Type equation here.

Solved Example 10

The dimensional formula of the density is….

a) ML2T-1 b) ML-3T0 c) a or b d) MLT

Steps:

Density = MassVolume = mv = ML3 = ML-3

- unit → kg.m-3 = kg /m3

Solved Example 11

The dimensional formula of the linear momentum is….

a) MLT-1 b) ML-3T6 c) a or b d) MLT

Steps:

Linear momentum= mass x velocity

PL = m v

=MLT-1

4162425334010-unit → Kg.m.s-1 = Kg.m/s

20859756985lefttopAndre-Marie AmpereIsaac Newton Kelvin

Solved Example 4

Vf = Vi = [Where Vf : final velocity, Vi : initial velocity, a:acceleration] is the relation?

a- right b- wrong

Steps: Vf= Vi + at

L.H.S= LT-1 R.H.S= LT + LT-2 .T

= LT-1 + LT-1

= 2LT-2

L.H.S=R.H.S

-Relation is right

Remember: -Any number has no dimension

Solved Example 5

From the physical relation: X= C1 + C2 t

( where: X is the distance in meters and t is the time in seconds)

Then the measuring units of the two quantities C1 & C2 are ………………. , ………….

a) m, m/sb) Kg, mc) a or b d) m , s

Steps:

L.H.S = X = L , so→ R.H.S = L

C1 = L = meter

C2t = L

C2 = LT = LT-1 = meter/second

38671508890In the opposite figure, a car moves with velocity ν on a curved path of radius r. If the acceleration of the car is calculated rom the relation; a = rn vm where m and n are numeral constants with no dimensions, then the magnitudes of m and n are ……………………. .

m

n

a)

1

-2

b)

1

-1

c)

2

-2

d)

2

-1

Solution

[a] = [rn vm ]

L T-2 = Ln (LT-1)m = Ln Lm T-m

L T-2 = Ln+m T-m

By comparing the two terminals of the equation : n + m=1

∴N= -1

∴The correct choice is (d)

Integration with mathematics:

You can revise the rules of expone