First slide
Dimensions
Question

The pair of quantities having same dimensions is

Moderate
Solution

Impulse = Force × time = [MLT -2][T] = [MLT-1]

Surface tension =  Force  length =MLT2[L]=ML0T2

Angular momentum
= Moment of inertia × angular velocity

= [ML2][T-1] = [ML2T-1]

Work = Force × distance = [MLT-2][L] = [ML2T-2]

Energy = [ML2T-2] Torque = Force × distance = [MLT-2][L] = [ML2T-2]  Youngs modulus

= Force / Area  Change in length / original length =MLT2/L2[L]/[L]=ML1T2

Hence, among the given pair of physical quantities work and torque have the same dimensions [ML2T-2].

 

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