Question

Given that force $(5\hat{i}+7\hat{j}-3\hat{k})N$ acts on a particle at position $(\hat{i}+\hat{j}-\hat{k})m$. Find torque of this force on the particle about origin

• A. $4\hat{i}-2\hat{j}+2\hat{k}$
• B. $2\hat{i}-3\hat{j}+4\hat{k}$
• C. $5\hat{i}-2\hat{j}+3\hat{k}$
• D. $6\hat{i}-4\hat{j}+4\hat{k}$

Answer 1

Answer: (A)

$4\hat{i}-2\hat{j}+2\hat{k}$

From the definition of torque, we have:

Torque, $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$
$=(\hat{i}+\hat{j}-\hat{k})\times (5\hat{i}+7\hat{j}-3\hat{k})$
$=\hat{i}(-3+7)-\hat{j}(-3+5)+\hat{k}(7-5)$
$\overrightarrow{\tau }=4\hat{i}-2\hat{j}+2\hat{k}$