Question

A force $\overrightarrow{F}=5\hat{i}+2\hat{j}-5\hat{k}$ acts on a particle whose position vector is $\overrightarrow{r}=\hat{i}-2\hat{j}+\hat{k}$. What is the torque about the origin?

• A. $8\hat{i}+10\hat{j}+12\hat{k}$
• B. $8\hat{i}+10\hat{j}-12\hat{k}$
• C. $8\hat{i}-10\hat{j}-8\hat{k}$
• D. $10\hat{i}-10\hat{j}-\hat{k}$

Answer 1

The correct option is A $8\hat{i}+10\hat{j}+12\hat{k}$

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

$\therefore$ $\overrightarrow{\tau }=(\hat{i}-2\hat{j}+\hat{k})\times (5\hat{i}+2\hat{j}-5\hat{k})$

Or $\overrightarrow{\tau }=(10-2)\hat{i}-(-5-5)\hat{j}+(2+10)\hat{k}$

$⟹$ $\overrightarrow{\tau }=8\hat{i}+10\hat{j}+12\hat{k}$