Which of the following pairs of physical quantites does not have same dimensional formula ?

Options

A. Work and torque
B. Angular momentum and Planck's constant
C. Tension and surface tension
D. Impulse and linear momentum

Answer

C

Explanation

a) Work = force `xx` distance
`=[MLT^(-2)] [ML^2 T^(-2)]`
Torque = force `xx` distance `=[ML^2 T^(-2)]`
b) Angular momentum
`=mvr = [M] [LT^(-1)][L] = [ML^2 T^(-2)]`
Planck.s constant
`=E/V = ([ML^2 T^(-2)])/([T^(-1)])` = `[ML^2 T^(-1)]`
c) Tension = force `= [MLT^(-2)]`
surface tension
`=("force")/("length") =([MLT^(-2)])/([L]= [ML^0 T^(-2)]`
d) Impulse = force `xx` time
`[MLT^(-2)][T] = [MLT^(-1)]`
Momentum = mass `xx` velocity= `[M] [LT^(-1)]= [MLT^(-1)]`
Note: One should not be confused with the similar form tension in both the physical quantities -surface tension and tension. Dimensional formula for both of them is not same.