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 `overset rarr(L_(1))` of particle 1 about `A` is `overset rarr(L_(1)) = mv (d_(1)) o.`
B. Angular momentum `overset rarr(L_(2))` of particle 2 about A is `overset rarr(L_(1)) = mv r_(2) o.`
C. Total angular momentum of the system about `A` is `overset rarr(L) = mv (r_(1) + r_(2))o.`
D. Total angular momentum of the system about `A` is `overset rarr(L) = mv (d_(2) - d_(1)) ox`
`o.` respresents a unit vector coming out of the page.
ox represents a unit vector going into the page.

Answer

A, D

Explanation

As angular momentum = linear momentum multiplied by perpendicular distance of particle from the axis of rotation, therefore, for particle 1,
`overset rarr(L_(1)) = mv (d_(1)) o.`, perpendicular to plane of page and directed upwards, and for particle 2.
`overset rarr(L_(2)) = mv (d_(2)) ox`, perpendicular to plane of page and directed inwards.
`:.` Total angular momentum of the system, `overset rarr(L) = overset rarr(L_(2)) - overset rarr(L_(1)) = mv(d_(2) - d_(1)) ox`
It would be perpendicualr to plane of page and directed inwards.