A particle of mass `m` is moving in yz-plane with a unifrom velocity `v` with its trajectory running parallel to +ve y-axis and intersecting z-axis at `z = a` Fig. The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is :

Options

A. `mv a hat(e)_(x)`
B. `2mv a hat(e)_(x)`
C. `ymv hat(e)_(x)`
D. `2y mv hat(e)_(x)`

Answer

B

Explanation

The initial velocity is `v_(1)= v hat(e)_(y)` and after reflection from the wall, the final velocity is `v_(f)= - v hat(e)_(y)`. The trajectory is described as position vector `vec(r)= y hat(e)_(y) + a hat(e)_(z)` Hence, the change in angular momentum is `vec(r) xx m (v_(f)- v_(j))= 2 mv a hat(e)_(x)`