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प्रश्न
A thin spherical shell lying on a rough horizontal surface is hits by a cue in such a way that the line of action passes through the centre of the shell. As a result, the shell starts moving with a linear speed \[\nu\] without any initial angular velocity. Find the linear speed of the shell after it starts pure rolling on the surface.
उत्तर
Initial angular momentum about point A,
\[L = mvR\]
Angular momentum about point A' after it starts pure rolling,
\[L' = I\omega + m\left( v \times R \right)\]
\[ = \frac{2}{3}m R^2 \left( \frac{v'}{R} \right) + mv'R\]
\[= \frac{5}{3}mv'R\]
As no external torque is applied, angular momentum will be conserved.
Therefore, we have
`L = L'`
\[\Rightarrow mvR = \frac{5}{3}mv'R\]
\[ \Rightarrow v' = \frac{3v}{5}\]
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