The pair having the same dimensions is: [PMT/NEET-1996]
a. Angular momentum, work
b. Work, torque
c. Potential energy, linear momentum
d. Kinetic energy, velocity

Solution

• Angular momentum
  $
  L = mvr = M(LT^{-1})L = ML^{2}T^{-1}
  $
• Work
  $
  W = F \cdot d = (MLT^{-2})L = ML^{2}T^{-2}
  $
• Torque
  $
  \tau = F \cdot r = (MLT^{-2})L = ML^{2}T^{-2}
  $
• Potential energy
  $
  U = mgh = M(LT^{-2})L = ML^{2}T^{-2}
  $
• Linear momentum
  $
  p = mv = M(LT^{-1}) = MLT^{-1}
  $
• Kinetic energy
  $
  K = \tfrac{1}{2}mv^{2} = M(LT^{-1})^{2} = ML^{2}T^{-2}
  $
• Velocity
  $
  v = LT^{-1}
  $

Comparison

• Angular momentum → $ML^{2}T^{-1}$
• Work → $ML^{2}T^{-2}$
• Torque → $ML^{2}T^{-2}$
• Potential energy → $ML^{2}T^{-2}$
• Linear momentum → $MLT^{-1}$
• Kinetic energy → $ML^{2}T^{-2}$
• Velocity → $LT^{-1}$

Work and Torque have the same dimensions.

Answer
b. Work, torque