question_answer

A force of -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: D

Solution :

\[\overset{\to }{\mathop{\tau }}\,=\overset{\to }{\mathop{\mathbf{r}}}\,\times \overset{\to }{\mathop{\mathbf{F}}}\,\]                 \[\overset{\to }{\mathop{\tau }}\,=(\widehat{\mathbf{i}}-\widehat{\mathbf{j}})\times (-F\widehat{\mathbf{k}})\]                 \[=F[(-\widehat{\mathbf{i}}\times \widehat{\mathbf{k}})+(\widehat{\mathbf{j}}\times \widehat{\mathbf{k}})]\]                 \[=F[\widehat{\mathbf{j}}+\widehat{\mathbf{i}}]=F[\widehat{\mathbf{i}}+\widehat{\mathbf{j}}]\]