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 ${\vec{L}}_1=mv{\vec{r}}_1\odot$
• B. Angular momentum ${\vec{L}}_2$ of particle 2 about $A$ is ${\vec{L}}_2=mv{\vec{r}}_2\odot$
• C. Total angular momentum of the system about is $\vec{L}=mv\left({\vec{r}}_1+{\vec{r}}_2\right)\odot$
• D. Total angular momentum of the system about $A$ is $\vec{L}=mv\left(d_2-d_1\right)\otimes$

Answer 1

Answer: (D)

Angular momentum of particle 1 about $A$ is
${\vec{L}}_1=mv{d}_1\odot$
Angular momentum of particle 2 about $A$ is
${\vec{L}}_2=mv{d}_2\otimes$
$\therefore$ Total angular momentum of the system about
$A$ is $\vec{L}={\vec{L}}_2-\vec{L}$ and $(\because L_1$ and ${\vec{L}}_2$ are in opposite directions) $\vec{L}=mv\left(d_2-d_1\right)\otimes$