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

From the defination of angular momentum,
`vec(L)= vec(r )xxvec(p)= rmv sin phi (-hat(k))`

Therefore, the magnitude of `L` is
`L=mvr sin phi= mvd`
Where `d= r sin phi` is the distanece of closets approach of the particle to the origin. Since `d` is same for both the particles, `L_(A)=L_(B)`