Question

Two physical quantities of which one is a vector and the other is a scalar having the same dimensional formula are

• A. work and energy
• B. torque and work
• C. impulse and momentum
• D. power and pressure

Answer 1

The correct option is B torque and work

Torque is the turning effect of force and is a vector quantity. It depends on the magnitude of the force and its perpendicular distance from the line of action.

($\tau =\overrightarrow{F}\times \overrightarrow{r}$)
Work done is the dot product of force and displacement vectors. Thus, work done is a scalar quantity.

($W=\overrightarrow{F}\cdot \overrightarrow{s}=Fscos\theta$)
Dimension of Torque is $\left[ML{T}^{-2}L\right]$ and work done is $\left[ML{T}^{-2}L\right]$.
Thus, the dimensions of Torque and work done are the same.