Question

Mention one scalar and one vector physical quantity having same dimensional formula.

Answer 1

Scalar and Vector quantities:

1. A physical quantity that only has a magnitude and no direction is called a scalar quantity.
2. A physical quantity that has both magnitude and direction is called a vector quantity.

Scalar and Vector quantity have the same dimensional formula:

1. Work: It can be said to be done when a force applied to an object causes it to move a certain distance.
2. It is a scalar quantity as it has no direction.
3. Dimensional formula of work:
   $$\begin{gathered} Work=Force\times Dis\tan ce \\ =\left[ML{T}^{-2}\right]\times \left[L\right] \\ =\left[M{L}^2{T}^{-2}\right] \end{gathered}$$
4. Torque: It can be defined as the turning effect of a force.
5. It is a vector quantity as it has a direction.
6. Dimensional formula of torque:
   $$\begin{gathered} Torque=Force\times PerpendicularDis\tan ce \\ =\left[ML{T}^{-2}\right]\times \left[L\right] \\ =\left[M{L}^2{T}^{-2}\right] \end{gathered}$$

Thus, one scalar and one vector physical quantity having the same dimensional formula is work and torque respectively.