Question

The time dependence of the position of a particle of mass $m=2$ is given by $\overrightarrow{r}\left(t\right)=2t\hat{i}-3t^2\hat{j}$. Its angular momentum, with respect to the origin at time $t=2$ is :

• A. $36\hat{k}$
• B. $-34(\hat{k}-\hat{i})$
• C. $48(\hat{i}+\hat{j})$
• D. $-48\hat{k}$

Answer 1

The correct option is D $-48\hat{k}$

$\overrightarrow{L}=m[\overrightarrow{r}\times \overrightarrow{v}]$
$m=2kg$
$\overrightarrow{r}=2t\hat{i}-3t^2\hat{j}$
$=4\hat{i}-12\hat{j}$ (At t = 2 sec)
$\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}=2\hat{i}-6t\hat{j}=2\hat{i}-12\hat{j}$
$\overrightarrow{r}\times \overrightarrow{v}=(4\hat{i}-12\hat{j})\times (2\hat{i}-12\hat{j})$
$=-24\hat{k}$
$\overrightarrow{L}=m(\overrightarrow{r}\times \overrightarrow{v})$
$=-48\hat{k}$