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Oblique Collision

A solid spher...

Question

A solid sphere of mass $m$ rolls down an inclined plane a height $h$ . The rotational kinetic energy of the sphere is $= \frac{2}{x} (m g h)$ . Find $x$ .
[Hint Mechanical energy will remain conserved]

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Solution

In case of pure rolling
$\frac{K_{R}}{K_{r}} = \frac{2}{5}$ for a solid sphere
$∴ K_{R} = \frac{2}{7}$ (total kinetic energy)
$= \frac{2}{7} (m g h)$

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