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Q.
The pair of quantities having same dimensions is
NEETNEET 2013Physical World, Units and Measurements
Solution:
Impulse = Force $\times$ time
$=[MLT^{-2}][T]=[MLT^{-1}]$
Surface tension$=\frac{\text{Force}}{\text{length}}$
$=\frac{[MLT^{-2}]}{[L]}=[ML^0T^{-2}]$
Angular momentum
= Moment of inertia $\times$ angular velocity
$=[ML^2][T^{-1}]=[ML^2T^{-1}]$
Work = Force $\times$ distance
$=[MLT^{-2}][L]=[ML^2T^{-2}]$
Energy $=[ML^2T^{-2}]$
Torque = Force $\times$ distance
$=[MLT^{-2}][L]=[ML^2T^{-2}]$
Young's modulus
$=\frac{\text{Force / Area}}{\text{Change in length / original length}}$
$=\frac{[MLT^{-2}]/[L^2]}{[L]/[L]}=[ML^{-1}T^{-2}]$
Hence, among the given pair of physical quantities work and torque have the same dimensions $[ML^2T^{-2}]$.