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Which pair of physical quantities does not share the same dimensions?

1. Torque and work
2. Momentum and Planck’s constant
3. Stress and Young’s modulus
4. Speed and (μ0ε0)⁻¹/2

Correct answer: Momentum and Planck’s constant

Solution

Torque and work are both M L^2 T^-2; stress and Young's modulus are both M L^-1 T^-2; speed and (mu0 eps0)^(-1/2) = c are both L T^-1. But momentum has dimensions M L T^-1 while Planck's constant has M L^2 T^-1, so this pair does not match.

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