Explanation

$Force = Mass\ \times acceleration$ $\therefore$ Dimensions of force $= \lbrack M\rbrack\left\lbrack LT^{- 2} \right\rbrack = \left\lbrack MLT^{- 2} \right\rbrack$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Power = \frac{Work}{Time}$ $\therefore$ Dimensions of power $= \frac{\left\lbrack ML^{2}T^{- 2} \right\rbrack}{\lbrack T\rbrack} = \left\lbrack {ML}^{2}T^{- 3} \right\rbrack$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Torque = Force\ \times displacement$ $\therefore$ Dimensions of torque $= \left\lbrack MLT^{- 2} \right\rbrack\lbrack L\rbrack = \left\lbrack ML^{2}T^{- 2} \right\rbrack$ And dimensions of energy $= \left\lbrack ML^{2}T^{- 2} \right\rbrack$ Hence, torque and energy have same dimensions.