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 `vecL_(1)` of a particle 1 about A is `vecL_(1)=mv vecr_(1)odot`
B. Angular momentum `vecL_(2)` of particle 2 about A is `vecL_(2)=mv vecr_(2)odot`
C. Total angular momentum of the system about A is `vecL=mv (vecr_(1)+vecr_(2))odot`
D. Total angular momentum of the system about A is `vecL=mv(d_(2)-d_(1))ox`
`ox` represents a unit vector going into the page, `odot` represent a unit vector coming out of the page

Answer

d

Explanation

Angular momenum of particle 1 about a is `vecL_(1)=mvd_(1)`
Angular momentum of particle 2 about A is
`vecL_(2)=mvd_(2)`
`therefore` Total angular momentum of the system about A is
`vecL=vecL_(2)-vecL_(1)` (`therefore L_(1)` and `L_(2)` are in opposite directions)
`vecL= mv(d_(2)-d_(1))`