question_answer

A force of \[\text{-F}\] \[\mathbf{\hat{k}}\] acts on 0, the origin of the coordinate system. The torque about the point \[(1,-1)\] is

A) \[F\,(\mathbf{\hat{i}-\hat{j}})\]                              

B) \[-F\,(\mathbf{\hat{i}}+\mathbf{\hat{j}})\]

C) \[F\,(\mathbf{\hat{i}}+\mathbf{\hat{j}})\]                         

D) \[-F\,(\mathbf{\hat{i}}-\mathbf{\hat{j}})\]

Correct Answer: C

Solution :

\[\vec{\tau }=\vec{r}\times \vec{F}\] \[\vec{\tau }=(\hat{i}-\hat{j})\times (-F\hat{k})\] \[=F[(-\hat{i}\times \hat{k})+(\hat{j}+\hat{k})]\] \[=F(\hat{j}+\hat{i}]=F[\hat{i}+\hat{j}]\]