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):

Explanation

As mass of two balls are equal, they exchange their velocities after collision.
`u_(A) =sqrt(2gh),u_(B)=sqrt(2g(4h)) = sqrt(8 gh) ,h_(A) = (u_(A)^(2))/(2g) = h` ,
`h_(B) =h+(v_(B)^(2) sin^(2) 60^@)/(2g) = h + (9h)/(4) = (13h)/(4)`
`(because(v_(B))^(2) -u_(B)^(2) =-2gh rArr v_(B)^(2) = u_(B)^(2) -2gh rArr v_(B)^(2)=6gh)`
`(h_(A))/(h_(B)) = (4)/(13)`.