A solid sphere of mass m, radius R is rolling without slipping on rough horizontal surface as shown in figure. It collides elastically with another identical sphere at rest. There is not friction between the two spheres. The linear velocity of first sphere after it again starts rolling without slipping is $\frac{N}{7} R ω .$ Find the value of N.

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Detailed Solution

Just after Impact, $L_{i}$ = when pure rolling begins, $L_{f}$

$L_{i} = L_{f} \Rightarrow \frac{2}{5} (m R^{2}) ω = \frac{2}{5} (m R^{2}) ω^{'} + m v^{'} R \Rightarrow v^{'} = \frac{2}{7} R ω$

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