Question

Figure shows to identical particles $1$ and $2$, each of mass $m$, moving in opposite directions with same speed $v$ along parallel lines. At a particular instant $r_1$ and $r_2$ are their respective position vectors drawn from point $A$ which is in the plane of the parallel lines. Choose the correct options.

• A. Angular momentum $I_1$ of particle $1$ about $A$ is $I=mv\left(d_1\right)\odot$
• B. Angular momentum $I_2$ of particle $2$ about $A$ is $I_2=mv{r}_2\odot$
• C. Total angular momentum of the system about $A$ is $I=mv(r_1+r_2)\odot$
• D. Total angular momentum of the system about $A$ is $I=mv(d_2-d_1)\otimes$

Answer 1

The correct option is D Total angular momentum of the system about $A$ is $I=mv(d_2-d_1)\otimes$

Angular momentum of particle 1 about A is

${\overrightarrow{L}}_1=mv{d}_1$

Angular momentum of particle 2 about A is

${\overrightarrow{L}}_2=mv{d}_2$

$\therefore$Total angular momentum of the system about A is

$\overrightarrow{L}={\overrightarrow{L}}_2-{\overrightarrow{L}}_1$

$L_1$ and $L_2$ are in opposite directions

$\overrightarrow{L}=mv(d_2-d_1)$ into the page.