Question

A Force $\overrightarrow{F}=4\hat{i}-10\hat{j}$ acts on a body at a point having position vector $-5\hat{i}-3\hat{j}$ relative to the origin whose co-ordinates are on the axis of rotation. The torque acting on the body about the origin is

• A. $38\hat{k}$
• B. $-25\hat{k}$
• C. $62\hat{k}$
• D. None of these

Answer 1

The correct option is C $62\hat{k}$

As we know
$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$
Here $\overrightarrow{r}=-5\hat{i}-3\hat{j}$
$\overrightarrow{F}=4\hat{i}-10\hat{j}$
$\Rightarrow \overrightarrow{\tau }=(-5\hat{i}-3\hat{j})\times (4\hat{i}-10\hat{j})$
$\Rightarrow \tau =50(i\times \hat{j})-12(j\times i)$
$\Rightarrow \overrightarrow{\tau }=50\hat{k}-12(-\hat{k})$
$\Rightarrow \overrightarrow{\tau }=62\hat{k}$