Question

Force $\hat{i}-2\hat{j}$ and -$\hat{i}+2\hat{j}$ act through the points whose position vectors are $\hat{k}$ and $3\hat{k}$. The vector sum of the moments (torque) of these forces about origin is :

• A. $-4\hat{i}-2\hat{j}$
• B. $\overrightarrow{0}$
• C. $2\hat{i}-4\hat{j}$
• D. $\hat{k}$

Answer 1

The correct option is A $-4\hat{i}-2\hat{j}$

Given,
$\overrightarrow{F_1}=\hat{i}-2\hat{j}$
$\overrightarrow{F_2}=-\hat{i}+2\hat{j}$
$\overrightarrow{r_1}=\hat{k}$
$\overrightarrow{r_2}=3\hat{k}$
Torque $\tau =\overrightarrow{r_1}\times \overrightarrow{F_1}+\overrightarrow{r_2}\times \overrightarrow{F_2}$
$\Rightarrow \tau =\hat{k}\times (\hat{i}-2\hat{j})+3\hat{k}\times (-\hat{i}+2\hat{j})=\hat{k}\times (\hat{i}-2\hat{j}+(-3\hat{i}+6\hat{j}\left)\right)=\hat{k}\times (-2\hat{i}+4\hat{j})$
$=(-2\hat{j}-4\hat{i})$