Two identical balls `A` and `B` are released from the position shown in Fig. They collide elastically with each other on the horizontal portion. The ratio of heights attained by `A` and `B` after collision is (neglect friction)

Options

A. `1:4`
B. `2:1`
C. `4:13`
D. `2:5`

Answer

C

Explanation

When the two balls collide with each other as the mass of the two balls is equal, they exchange their velocities on colliding elasticaslly. Let the speed of the ball B when it reaches back ot the initial position be `v`. then
`4mgh=1/2mv^(2)+mghimpliesv=sqrt(6gh)`
Height reached by particle `B` (from highest point the incline)
`H_(B)=(v^(2)sin^(2)60^(@))/(2g)=(9h)/4`, total height `=h+(9h)/4=(13h)/4`
after collision the partcle `A` reaches the maximum height `=h`
Ratio `=H_(A)/H_(B)=4/13`