Question

Identify three physical quantities which are having same dimensions.

Answer 1

Dimensions and dimensional formula:

1. Any physical quantity can be represented in terms of the fundamental quantities.
2. The powers of these fundamental quantities that appear in the expression of a physical quantity are termed dimensions.
3. The formula representing these dimensions is called the dimensional formula.

Three physical quantities have the same dimensions:

1. Work: It can be said to be done when a force applied to an object causes it to move a certain distance.
   Dimensional formula of work:
   $$\begin{gathered} Work=Force\times Dis\tan ce \\ =\left[ML{T}^{-2}\right]\times \left[L\right] \\ =\left[M{L}^2{T}^{-2}\right] \end{gathered}$$
2. Torque: It can be defined as the turning effect of a force.
   Dimensional formula of torque:
   $$\begin{gathered} Torque=Force\times PerpendicularDis\tan ce \\ =\left[ML{T}^{-2}\right]\times \left[L\right] \\ =\left[M{L}^2{T}^{-2}\right] \end{gathered}$$
3. Energy: It can be defined as the capacity to do work.
   There are different forms of energy like kinetic energy, potential energy, etc. We can use any of these to find its dimensions.
   Dimensional formula of potential energy:
   $$\begin{gathered} P.E.=Mass\times Accelerationduetogravity\times Height \\ =\left[M\right]\times \left[L{T}^{-2}\right]\times \left[L\right] \\ =\left[M{L}^2{T}^{-2}\right] \end{gathered}$$

Thus, the three physical quantities which are having same dimensions are Work, Torque, and Energy.