Question

A force $(5\hat{i}+7\hat{j}-3\hat{k})N$ acts on a particle at position $(\hat{i}+\hat{j}-\hat{k})m$. Find torque of this force on the particle about origin.

• A. $(4\hat{i}+2\hat{j}+2\hat{k})N-m$
• B. $(4\hat{i}-2\hat{j}+2\hat{k})N-m$
• C. $(-4\hat{i}+2\hat{j}-2\hat{k})N-m$
• D. $(10\hat{i}-8\hat{j}+12\hat{k})N-m$

Answer 1

The correct option is B $(4\hat{i}-2\hat{j}+2\hat{k})N-m$

We know that, Torque $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$--------- (1)

Given, $\overrightarrow{F}=5\hat{i}+7\hat{j}-3\hat{k}$

and $\overrightarrow{r}=\hat{i}+\hat{j}-\hat{k}$

(1) => $\overrightarrow{\tau }=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 1& -1\\ 5& 7& -3\end{array}\right|$

=$\hat{i}(-3+7)-\hat{j}(-3+5)+\hat{k}(7-5)$

$\overrightarrow{\tau }=(4\hat{i}-2\hat{j}+2\hat{k})Nm$