OnlineCBT
Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीGiven below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If the total external force acting on a system of particles is zero, the total external torque on the system is independent of the choice of the origin. Reason (R): For any displacement \( \mathbf{a} \) of the origin, the change in the total torque is given by \( -\mathbf{a} \times \sum \mathbf{F}_{\text{ext}} \). In the light of the above statements, choose the correct answer from the options given below:
Correct answer · Option 1
Both (A) and (R) are true and (R) is the correct explanation of (A).
Explanation
Let \( \mathbf{r}'_i = \mathbf{r}_i - \mathbf{a} \). Then \( \boldsymbol{\tau}' = \sum (\mathbf{r}_i - \mathbf{a}) \times \mathbf{F}_i = \boldsymbol{\tau} - \mathbf{a} \times \sum \mathbf{F}_i \). Since \( \sum \mathbf{F}_i = 0 \), \( \boldsymbol{\tau}' = \boldsymbol{\tau} \). Hence both (A) and (R) are true and (R) correctly explains (A).
