Out of the following, the only pair that does not have identical dimensions is: [PMT/NEET-1998]
a. Angular momentum and Planck’s constant
b. Moment of inertia and moment of a force
c. Work and torque
d. Impulse and momentum

Solution

• Angular momentum: $ML^{2}T^{-1}$
• Planck’s constant (h): Energy × time = $(ML^{2}T^{-2})(T) = ML^{2}T^{-1}$
  → Same
• Moment of inertia: $I = MR^{2} = ML^{2}$
• Moment of a force (torque): $ML^{2}T^{-2}$
  → Different
• Work: $ML^{2}T^{-2}$
• Torque: $ML^{2}T^{-2}$
  → Same
• Impulse: $MLT^{-1}$
• Momentum: $MLT^{-1}$
  → Same

Answer
b. Moment of inertia and moment of a force