Two identical balls `A and B` arereleased from the positions shown in figure. They collide elasticallly on horizontal position `MN` . The ratio of the heightsattaned by `A and B` after collisuion 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 in equal, they exchange their velocites on colliding eleastically. Let the speed of the ball `B` when it reaches back to the initial position be `v`. Then
`4 mgh=(1)/(2)mv^(2)+mghrArrv=sqrt(6 mgh)`
Height reached by particle `B` (from highest point on the incline) is `H_(B)=(v^(2)sin^(2)60^(@))/(2g)=(9h)/(4)`,
Total height `=h+(9h)/(4)=(13h)/(4)`
After collision the particle `A` reaches the maximum height `=h`
Ratio `=(H_(A))/(H_(B))=(4)/(13)`