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Question: Two identical balls A and B are released from the position shown in the figure. They collide elastic...

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

A

1 : 4

B

2 : 1

C

4 : 13

D

2 : 5

Answer

4 : 13

Explanation

Solution

When the two balls collide with each other as the mass of the two balls is equal they exchange their velocities on colliding elastically speed of the ball B when it reaches back to the initial position

3mgh = 12\frac{1}{2}mv2 ̃ v = 6gh\sqrt{6gh}

Height reached by the particle B (from highest point on the incline)

HB = 9h4\frac{9h}{4} ; total height = h + 9h4=13h4\frac{9h}{4} = \frac{13h}{4}

After collision when particle reaches the max. height = h

Ratio = HAHB=413\frac{H_{A}}{H_{B}} = \frac{4}{13}