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Q.

Two identical balls of equal masses A and B, are lying on a smooth surface as shown in figure .Ball A hits the ball B(which is at rest )with a velocity $v = 16 m / s$ .What should be the minimum value of coefficient of restitution $e$ between A and B so that B just reaches the highest point of inclined plane: (Take $g = 10 m / s^{2}$ )

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a

$\frac{2}{3}$

b

$\frac{1}{2}$

c

$\frac{1}{4}$

d

$\frac{1}{3}$

answer is B.

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Detailed Solution

For B to just reach highest point of inclined plane
$\frac{1}{2} m v^{2} = m g (5)$
$\frac{v^{2}}{2} = 50$
$v^{2} = 100$
$v = 10 m / s$
Where v is velocity of B after collision,
$10 = \frac{(1 + e) m}{2 m} (16) + 0$
$10 = (1 + e) 8$
$\Rightarrow 1 + e = \frac{5}{4}$
$\Rightarrow e = \frac{5}{4} - 1 = \frac{1}{4}$

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