question_answer

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

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

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 :

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