Question

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

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

Answer: (C)

$-1$

For conservation of angular momentum, net torque is zero.

$\tau =\overrightarrow{r}\times \overrightarrow{F}=0$

$-(12+12\alpha )\hat{j}+(6+6\alpha )\hat{k}=0\Rightarrow \alpha$ = $-1$