Two identical balls A and B are released from the positions shown in the figure. They collide elastically on horizontal portion MN. The ratio of heights attained by A and B after collision will be (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`