Question

A force $\overrightarrow{F}=(\hat{i}-\hat{j})N$ acts at $P$. the torque of the force $\overrightarrow{F}$ about $O$ is

• A. $2\hat{i}-3\hat{j}+5\hat{k}$
• B. $-2\hat{i}-3\hat{j}-5\hat{k}$
• C. $\hat{i}-\hat{j}-4\hat{k}$
• D. $-2\hat{i}-2\hat{j}-5\hat{k}$

Answer 1

The correct option is D $-2\hat{i}-2\hat{j}-5\hat{k}$

Given,

$F=i-j$

$P=i+3j-k$

$O=-i+k$

$\Rightarrow OP=(-i+k)-(i+3j-k)$

$\therefore OP=\overrightarrow{r}=-2i-3j+2k$

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$

$\overrightarrow{\tau }=(-2i-3j+2k)\times (i-j)$

$\therefore \overrightarrow{\tau }=-2i-2j-5k$