Question

Figure shows two identical particles 1 and 2 , each of mass $m$, moving in opposite directions with same speed $\vec{v}$ along parallel lines. At a particular instant, $\vec{r}_{1}$ and $\vec{r}_{2}$ are their respective position vectors drawn from point $A$ which is in the plane of the parallel lines. Which of the following is the correct statement?
[Here, $\otimes$ represents a unit vector going into the page and $\odot$ represents a unit vector coming out of the page.]

• A. Angular momentum $\vec{L}_{1}$ of particle 1 about $A$ is $\vec{L}_{1}=m v \vec{r}_{1} \odot$
• B. Angular momentum $\vec{L}_{2}$ of particle 2 about $A$ is $\vec{L}_{2}=m v \vec{r}_{2} \odot$
• C. Total angular momentum of the system about is $\vec{L}=m v\left(\vec{r}_{1}+\vec{r}_{2}\right) \odot$
• D. Total angular momentum of the system about $A$ is $\vec{L}=m v\left(d_{2}-d_{1}\right) \otimes$

Answer 1

Answer: (D)

Angular momentum of particle 1 about $A$ is
$\vec{L}_{1}=m v d_{1} \odot$
Angular momentum of particle 2 about $A$ is
$\vec{L}_{2}=m v d_{2} \otimes$
$\therefore $ Total angular momentum of the system about
$A$ is $\vec{L}=\vec{L}_{2}-\vec{L}$ and $\left(\because L_{1}\right.$ and $\vec{L}_{2}$ are in opposite directions) $\vec{L}=m v\left(d_{2}-d_{1}\right) \otimes$