question_answer

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

A)  \[F\left( \widehat{i}-\widehat{j} \right)\]                           

B)  \[-F\left( \widehat{i}+\widehat{j} \right)\]

C)  \[F\left( \widehat{i}+\widehat{j} \right)\]                          

D)  \[-F\left( \widehat{i}-\widehat{j} \right)\]

Correct Answer: C

Solution :

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