A particle of mass `m` moves in the `XY` plane with a velocity `v` along the straight line `AB`. If the angular momentum of the particle with respect to origin `O` is `L_(A)` when it is at A and `L_(B)` when it is at B, then

Options

A. `L_A gt L_B`
B. `L_A = L_B`
C. the relationship between `L_A` and `L_B` depends upon the slope of the line `AB`.
D. `L_A lt L_B`

Answer

B

Explanation

(b) From the defination of angular momentum,
`vec L = vec r xx vec p = rmv sin phi (- hat k)`
Therefore, the magnitude of `L` is
`L = mvr sin phi = mvd`
where `d = r sin phi` is the distance of closest approach of the particle to the origin. As `d` is the same for both the cases, hence `L_A = L_B`.
.