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

When the two balls collide with each other ,as the mass of the two balls is equal, they exchange their velocities on colliding elastically. Let the speed of the ball B when it reaches back to the initial position be v. Thentotal energy of B after collision=(KE+PE)at point B  4mgh = 12 mv2 + mgh  ⇒v=6ghHeight reached by particle B(from highest point on the incline) is , ball is expected to have projectile motion from point Bmaximum height reached by ball from point B is HB=v2sin2θ2g HB=v2sin26002g HB=(6gh)(32)22g HB=9h4, total height from the bottom reached by ball B = h+ 9h4 =  13h4After collision the particle A reaches the maximum height = hRatio =  due to exchange of velocity, ball A will be able to reach maximum height h but ball B reaches maximum height =13h4 HAHB=h13h4 HAHB=413