Question

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

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

Answer 1

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

Position vector $\overrightarrow{r}=\overrightarrow{PO}=\overrightarrow{0}-(1\hat{i}-1\hat{j})=-\hat{i}+\hat{j}$

Torque about point P, $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$

$\therefore$ $\overrightarrow{\tau }=(-\hat{i}+\hat{j})\times (-F\hat{k})$

OR $\overrightarrow{\tau }=F\left[\right(\hat{i}\times \hat{k})-(\hat{j}\times \hat{k}\left)\right]=F[-\hat{j}-\hat{i}]$

$⟹$ $\overrightarrow{\tau }=-F[\hat{i}+\hat{j}]$