Question

A force $F=(5\sqrt{3}\hat{i}+5\hat{j})\text{N}$ is acting on a body at point $(1,1)\text{m}$. Calculate torque of this body w.r.t to point $(1,0)\text{m}$

• A. $-5\sqrt{3}\hat{k}$
• B. $\sqrt{3}\hat{k}$
• C. $5\sqrt{3}\hat{k}$
• D. $-\sqrt{3}\hat{k}$

Answer 1

The correct option is A $-5\sqrt{3}\hat{k}$

$F=(5\sqrt{3}\hat{i}+5\hat{j})N$ and $\overrightarrow{r}=(0\hat{i}+1\hat{j})$
$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 0& 1& 0\\ 5\sqrt{3}& 5& 0\end{array}\right|$
$\overrightarrow{\tau }=-5\sqrt{3}\hat{k}\text{Nm}$