Question

A particle is at rest at a point $(4,3,0)$. Due to an impulse, it gets linear momentum $\overrightarrow{P}=\hat{i}+2\hat{j}$. The angular momentum of the particle about the origin is

• A. $11(-\hat{k})$
• B. $5(-\hat{k})$
• C. $5\hat{k}$
• D. $11\left(\hat{k}\right)$

Answer 1

The correct option is C $5\hat{k}$

Given,
Linear momentum $\overrightarrow{P}=\hat{i}+2\hat{j}$
Position vector $\overrightarrow{r}$ (about origin)
$\overrightarrow{r}=(4-0)\hat{i}+(3-0)\hat{j}$
$\overrightarrow{r}=4\hat{i}+3\hat{j}$
As we know,
Angular momentum $\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$
(where $\overrightarrow{p}$ = linear momentum)
$\overrightarrow{L}=(4\hat{i}+3\hat{j})\times (\hat{i}+2\hat{j})$
$\overrightarrow{L}=\left[8\right(\hat{i}\times \hat{j})+3(\hat{j}\times \hat{i}\left)\right]$
$\overrightarrow{L}=8\left(\hat{k}\right)+3(-\hat{k})$
$\overrightarrow{L}=5\hat{k}$