Question

$\overrightarrow{F}=a\hat{i}+3\hat{j}+6\hat{k}$ and $\overrightarrow{r}=2\hat{i}-6\hat{j}-12\hat{k}$. The value of ${}^{\prime }{a}^{\prime }$ for which the angular momentum is conserved is

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (A)

-1

We know,

For angular momentum to be conserved about a point,

Torque on a body should be zero about that point.

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

$\overrightarrow{\tau }=(ai+3j+6k)\times (2i-6j-12k)$

$\overrightarrow{\tau }=0i+(-12a-12)j+(-6a-6)k$

$\overrightarrow{\tau }=0$,

$a=-1$

Option $\text{A}$ is the correct answer