Question: Which one has the dimensions different from the remaining three: [PMT/NEET-1988]
a. Power
b. Work
c. Torque
d. Energy

Solution

Work:
$
[W] = [\text{Force} \times \text{Distance}] = ( MLT^{-2}) \times L = ML^{2}T^{-2}
$

Torque:
$
[\tau] = [\text{Force} \times \text{Perpendicular distance}] = ( MLT^{-2}) \times L = ML^{2}T^{-2}
$

Energy:
(same as work)
$
[E] = ML^{2}T^{-2}
$

Power:
$
[P] = \frac{\text{Work}}{\text{Time}} = \frac{ML^{2}T^{-2}}{T} = ML^{2}T^{-3}
$

Observation:

• Work, Torque, and Energy have same dimensions ($ML^{2}T^{-2}$).
• Power is different ($ML^{2}T^{-3}$).

Answer:
a. Power