Question

Which of the following pairs of physical quantities has the same dimensions?

• A. Work and power
• B. Momentum and energy
• C. Force and power
• D. Work and energy

Answer 1

Answer: (D)

Work and energy

The dimension of the various quantities are:

Work : $\left[M{L}^2{T}^{-2}\right]$

Power: $\left[M{L}^2{T}^{-3}\right]$

Momentum: $\left[ML{T}^{-1}\right]$

Energy: $\left[M{L}^2{T}^{-2}\right]$

Force: $\left[ML{T}^{-2}\right]$

So, the quantities with the same dimensional formula are $work$ and $energy$.

Option $\left(D\right)$ is correct.