A ball `A` of mass `1 kg` , moving with a speed of `12 m//s` , collides obliquely and elasticity with another ball `B` which was initially at rest. Ball `A` then moves off at the right angle to its initial direction with a speed of `5 m//s`. The momentum of ball `B` after the collision is

Options

A. `5 kg m//s`
B. `11 kg m//s`
C. `13 kg m//s`
D. `17 kg m//`

Answer

C

Explanation

Momentum conservation :
`x`-direction : `1 xx 12 = mv cos theta rArr mv cos theta = 12`
`y`-direction : `0 = 1 xx 5 - mv sin theta rArr mv sin theta = 5`
`mv = sqrt((mv cos theta)^(2) + (mv sin theta)^(2))`
`= sqrt((12)^(2) + (5)^(2)) = 13 kg m//s`