Question

A particle of mass $2 \,kg$ is moving such that at time $t$, its position, in meter, is given by $\vec{r}\left(t\right)=5\hat{i}-2t^{2}\,\hat{j}$. The angular momentum of the particle at $t = 2s$ about the origin in $kg \,m^{-2}\, s^{-1}$ is :

• A. $-80\hat{k}$
• B. $\left(10\hat{i}-16\hat{j}\right)$
• C. $-40\hat{k}$
• D. $40\hat{k}$

Answer 1

Answer: (A)

Angular momentum $L=m (v \times r)$
$=2\,kg\left(\frac{dr}{dt}\times r\right)=2\,kg \left(4t\, j \times 5i - 2t^{2}\, \hat{j}\right)$
$=2\,kg\left(-20\,t\,\hat{k}\right)==2\,kg \times-20\times2\,m^{-2}\,s^{-1}\hat{k}$
= $-80\,\hat{k}$