The pair of quantities having same dimensions is
Impulse and Surface Tension
Angular momentum and Work
Work and Torque
Young’s modulus and Energy
Impulse = Force × time = [MLT -2][T] = [MLT-1]
Surface tension = Force length =MLT−2[L]=ML0T−2
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] Young’s modulus
= Force / Area Change in length / original length =MLT−2/L2[L]/[L]=ML−1T−2
Hence, among the given pair of physical quantities work and torque have the same dimensions [ML2T-2].