Question

A force $\overrightarrow{F}=\alpha \hat{i}+3\hat{j}+6\hat{k}$ is acting at a point $\overrightarrow{r}=2\hat{i}-6\hat{j}-12\hat{k}$. The value of $\alpha$ for which angular momentum about origine is conserved is

• A. $1$
• B. $-1$
• C. $2$
• D. Zero

Answer 1

The correct option is B $-1$

For conservation of angular momentum about origin, external torque acting about origin should be zero.

$\therefore$ Torque $=r\times F$

$\Rightarrow (2\hat{i}-6\hat{j}-12\hat{k})\times (\alpha \hat{i}+3\hat{j}+6\hat{k})=(-36+36)\hat{i}+(-12\alpha -12)\hat{j}+(6+6\alpha )\hat{k}=0$ $\Rightarrow \alpha =-1$