Question

A force $F(-\hat{k})$ acts on the origin of the co-ordinate system. The torque about the point (1 , -1 ) is

• A. $F(\hat{i}-\hat{j})$
• B. $-F(\hat{i}+\hat{j})$
• C. $F(\hat{i}+\hat{j})$
• D. $-F(\hat{i}-\widehat{j)}$

Answer 1

The correct option is B $-F(\hat{i}+\hat{j})$

$\begin{array}{c}\overrightarrow{r}=\left(0-1\right)\overrightarrow{i}+\left(0+1\right)\overrightarrow{j}\\ =-\overrightarrow{i}+\overrightarrow{j}\\ \overrightarrow{F}=F\left(-\hat{K}\right)\\ \tau =\left(\overrightarrow{r}\times \overrightarrow{F}\right)\\ =F\left(-\hat{i}+\hat{j}\right)\times \left(\overrightarrow{k}\right)\\ =F\left(\hat{j}-\hat{i}\right)\\ =-F\left(\hat{i}+\hat{j}\right)\\ Hence,\\ optionBiscorrectanswer.\end{array}$