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 hate_(x)`
B. `2mv a hate_(x)`
C. `ymv a hate_(x)`
D. `2ymv a hate_(x)`

Answer

B

Explanation

Linear momentum of particle before colliding `= m overset rarr(v) = mv hate_(y)`
Linear momentum of particle after it bounces `= m overset rarr(v) = - mvhate_(y)`
Change in linear momentum, `Delta overset rarr(p) = - m overset rarr(v) - (m overset rarr(v)) = - 2m overset rarr(v) = - 2mv hate_(y)`
Change in angular momentum `Delta overset rarr(L) = overset rarr(r ) xx Delta overset rarr(p), where overset rarr(r) = (y hate_(y) + a hate_(z))`
`= (y hate_(y) + a hate_(z)) xx (-2mv hate_(y)) = 2mv a hate_(x)`.