Dimensional analysis MCQ: Identify the pair of physical quantities that do not share identical dimensions. Out of the following pairs, determine which pair has different dimensional formula; assume standard M–L–T system for mechanics quantities. Choose the correct option.

Given data

• We compare dimensions of four pairs under the M–L–T system.

Concept/ApproachUse dimensional formulae: Force = MLT^-2; Work/Energy = ML²T^-2; Power = ML²T^-3; Impulse = change of momentum = MLT^-1; Pressure/Stress = ML^-1T^-2; Torque (moment of force) = ML²T^-2.

Step-by-step checkWork vs torque ⇒ both ML²T^-2 (identical).Impulse vs momentum ⇒ both MLT^-1 (identical).Pressure vs stress ⇒ both ML^-1T^-2 (identical).Power vs energy ⇒ ML²T^-3 vs ML²T^-2 (different).

Common pitfallsConfusing torque with power; torque shares dimensions with work/energy, but power includes per-unit-time.

Final AnswerPower and energy