Question

The pair of quantities having same dimensions is

• A. Impulse and Surface Tension
• B. Angular momentum and Work
• C. Work and Torque
• D. Young's modulus and Energy

Answer 1

Answer: (C)

Impulse = Force $\times$ time
$=[ML{T}^{-2}][T]=[ML{T}^{-1}]$
Surface tension$=\frac{\text{Force}}{\text{length}}$
$=\frac{[ML{T}^{-2}]}{[L]}=[M{L}^0{T}^{-2}]$
Angular momentum
= Moment of inertia $\times$ angular velocity
$=[M{L}^2][T^{-1}]=[M{L}^2{T}^{-1}]$
Work = Force $\times$ distance
$=[ML{T}^{-2}][L]=[M{L}^2{T}^{-2}]$
Energy $=[M{L}^2{T}^{-2}]$
Torque = Force $\times$ distance
$=[ML{T}^{-2}][L]=[M{L}^2{T}^{-2}]$
Young's modulus
$=\frac{\text{Force / Area}}{\text{Change in length / original length}}$
$=\frac{[ML{T}^{-2}]/[L^2]}{[L]/[L]}=[M{L}^{-1}{T}^{-2}]$
Hence, among the given pair of physical quantities work and torque have the same dimensions $[M{L}^2{T}^{-2}]$.