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

Answer: (C)

Here, $\vec{F}=-F\hat{k},\vec{r}=\hat{i}-\hat{j}$
Torque $\vec{\tau }=\vec{r}\times \vec{F}$
$\vec{\tau }=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -1& 0\\ 0& 0& -F\end{array}\right|$
$\vec{\tau }=\hat{i}\left(F-0\right)-\hat{j}\left(-F-0\right)+\hat{k}\left(0-0\right)$
$=F\hat{i}+F\hat{j}$
$\vec{\tau }=F\left(\hat{i}+\hat{j}\right)$