# The time dependence of the position of a particle of mass $m=2$ is given by  $\vec{r}\left ( t \right )= 2t\hat{i}-3t^{2}\hat{j}$ Its angular momentum with respect to the origin , at time $t=2$is:Option 1)$48\left ( \hat{i +\hat{j}} \right )$Option 2)$36\hat{k}$Option 3)$-34\left ( \hat{k} -\hat{i}\right )$Option 4)$-48\hat{k}$

$\vec{r}=2t\hat{i}-3t^{2}\hat{t}$

$m=2kg$

$\vec{L}=m \left [ \hat{r}\times \hat{v} \right ]$

$\vec{v}=\frac{d\left ( \vec{r} \right )}{dt}$

at $t=2sec$

$\vec{V}=2\hat{i}-12\hat{j}$

$\vec{r } =4\hat{i}-12\hat{j}$

$\left [ \vec{r}\times \vec{v}\right ]=\left ( 4\hat{i} -12\hat{j}\right )\times \left ( 2\hat{i}-12 \hat{j}\right )=-24\hat{k}$

$\vec{L}=m \left [ \vec{r}\times \vec{v} \right ]$

$\vec{L}=-48\hat{K}$

Option 1)

$48\left ( \hat{i +\hat{j}} \right )$

Option 2)

$36\hat{k}$

Option 3)

$-34\left ( \hat{k} -\hat{i}\right )$

Option 4)

$-48\hat{k}$

Exams
Articles
Questions