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 ?
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Options

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 (vec r_1 + vec r_2) odot`
D. Total angular momentum of the system about `A` is `vec L = mv(d_2 - d_1) otimes`
[Here, `otimes` represents a unit vector going into the page and `odot` represents a unit vector coming out of the page].

Answer

D

Explanation

(d) Angular momentum of particle `1` about `A` is
`vec L_1 = mvd_1 odot`
Angular momentum of particle `2` about `A` is
`vec L_2 = mvd_2 otimes`
:. Total angular momentum of the system about `A` is `vec L = vec L_2 - vec L` and `(because L_1 and L_2` are in opposite directions) `vec L = mv(d_2 - d_1) otimes`.