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 origin of co-ordinate 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 $62\hat{k}$

Force acting on the body $\overrightarrow{F}=4\hat{i}-10\hat{j}$

Position vector $\overrightarrow{r}=-5\hat{i}-3\hat{j}$

Thus, torque $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$

$⟹\overrightarrow{\tau }=(-5\hat{i}-3\hat{j})\times (4\hat{i}-10\hat{j})=62\hat{k}$