Question

The position of a particle is given by $\overrightarrow{r}=(\hat{i}+2\hat{j}-\hat{k})\text{m}$ and linear momentum as $\overrightarrow{p}=(3\hat{i}+4\hat{j}-2\hat{k})\text{kg-m/s}$. The angular momentum of the particle about the origin $(0,0,0)$ is perpendicular to

• A. $x-$ axis
• B. $y-$ axis
• C. $z-$ axis
• D. $xz-$ plane

Answer 1

The correct option is A $x-$ axis

Angular momentum about the origin $(0,0,0)$ is given by,
$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$



$\Rightarrow \overrightarrow{L}=(-4+4)\hat{i}-(-2+3)\hat{j}+(4-6)\hat{k}$
$\Rightarrow \overrightarrow{L}=(-\hat{j}-2\hat{k}){\text{kg-m}}^2\text{/s}$
It indicates that the angular momentum vector is in $yz-$ plane, and we know that $yz-$ plane is perpendicular to $x-$ axis.


Hence, the angular momentum $\overrightarrow{L}$ is perpendicular to $x-$ axis.