Ball A of mass m after sliding from an inclined plane strikes elastically with another ball B of mass 3m at rest. The minimum height h, so that the ball B just completes the circular portion of the surface at C, will be nR then value of n (all surfaces are smooth)

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answer is 10.

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Detailed Solution

$\begin{matrix} u_{A} = \sqrt{2 gh}, v_{B} = \frac{2 m_{1} u_{A}}{m_{1} + m_{2}} = \frac{u_{A}}{2} = \frac{\sqrt{2 gh}}{2} \\ To complete vertical circle, v_{B}^{2} = 5 gR \Rightarrow \\ \frac{2 gh}{4} = 5 gR ∴ h = 10 R \end{matrix}$

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