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Ball A of mass m, after sliding from an inclined plane, strikes elastically another ball B of same mass at rest. Find the minimum height h so that ball B just completes the circular motion of the surface at C. (All surfaces are smooth.)

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$h = \frac{5}{2} R$

$h = 2 R$

$h = \frac{2}{5} R$

$h = 3 R$

answer is A.

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Detailed Solution

mgh = $\frac{1}{2} m v^{2}$ +2mgR $\Rightarrow g h = \frac{v^{2}}{2} + 2 g R$

Required velocity at the top $v = \sqrt{g R}$ $\Rightarrow g h = \frac{g R}{2} + 2 g R$ $\Rightarrow h = \frac{5}{2} R$

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