Two identical balls A and B lie on a smooth horizontal surface, which gradually merge into a curve to a height 3.2m Ball A is given a velocity $10 {ms}^{- 1}$ to collide head on with ball B. Which then takes up the curved path? The minimum coefficient of restitution ‘e’ for the collision between A and B in order that of B reaches the highest point P of curve is $(given g = 10 {ms}^{- 2})$

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1/2

3/5

3/4

1/4

answer is B.

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Detailed Solution

Total energy at B = Total energy at P

$\frac{1}{2} {mv}_{2}^{2} = mgh$

$v_{2} = \sqrt{2gh}$

$v_{2} = \sqrt{2 (10) 3.2}$

$v_{2} = \sqrt{64}$

$v_{2} = 8 m/s$

$v_{2} = (1 + e) \frac{u_{1}}{2}$

[ $∵ m_{1} = m_{2}$ in inelastic collision]

$8 = (1 + e) \frac{10}{2}$

$\frac{8}{5} = (1 + e) \Rightarrow e = \frac{8}{5} - 1$

$e = \frac{3}{5}$

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