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