Question

A force $F=2\hat{i}+3\hat{j}-\hat{k}$ acts at a point (0,0,2)then the magnitude of torque about origin is:

• A. $6$
• B. $7.21$
• C. $\sqrt{52}$
• D. None of these

Answer 1

Answer: (B), (C)

The correct options are
B $7.21$
C $\sqrt{52}$

Position vector $\overrightarrow{r}=2\hat{k}$

Force is given as $\overrightarrow{F}=2\hat{i}+3\hat{j}-\hat{k}$

Torque about origin $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$

$⟹\overrightarrow{\tau }=2\hat{k}\times (2\hat{i}+3\hat{j}-\hat{k})=-6\hat{i}+4\hat{j}$

Magnitude of torque $|\overrightarrow{\tau }|=\sqrt{6^2+4^2}=\sqrt{52}Nm=7.21Nm$