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  4. A heavy solid sphere is thrown on a horizontal rough surface with initial velocity u without rolling. What will be its speed, when it starts pure rolling motion?

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Q. A heavy solid sphere is thrown on a horizontal rough surface with initial velocity $u$ without rolling. What will be its speed, when it starts pure rolling motion?

System of Particles and Rotational Motion

Solution:

Using angular momentum conservation
$m u r=m v r+\frac{2}{5} m r^{5}\left(\frac{v}{r}\right)$
$u=7 \frac{V}{5}$
$v=\frac{5 u}{7}$