Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Torque and work possess identical dimensional formulas \( [M L^2 T^{-2}] \), yet work is a scalar quantity whereas torque is a vector quantity. Reason (R): Torque is defined via the vector cross product \( \mathbf{r} \times \mathbf{F} \), giving it an explicit directional character, whereas work is defined via the scalar dot product \( \mathbf{F} \cdot \Delta\mathbf{r} \). In the light of the above statements, choose the correct answer from the options given below:

1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
3. (A) is true but (R) is false.
4. (A) is false but (R) is true.