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In the figure shown, the two identical balls of mass M and radius R each, are placed in contact with each other on a frictionless horizontal surface. A third ball of mass M and radius R/2 is coming down vertically and has a velocity $v_{0}$ when it simultaneously hits the two balls. The third ball comes to rest after collision. Then the speed of the each of the bigger balls just after collision is $v_{0} / \sqrt{n}$ (Assume that there is no friction between the balls) where ‘n’ is ___

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answer is 5.

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Detailed Solution

$2 Jcos θ = {mV}_{0} . . . . (1)$

$Jsin θ = mV$

$\frac{(2)}{(1)} \Rightarrow \frac{\sin θ}{2 \cos θ} = \frac{V}{V_{0}} \Rightarrow V = \frac{V_{0}}{2} \tan θ = \frac{V_{0}}{2} \frac{\sin θ}{\cos θ}$

$V = \frac{V_{0}}{2} \frac{2}{3} \cdot \frac{3}{\sqrt{5}} = \frac{V_{0}}{\sqrt{5}}$

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