Solve the following :

Question:

A sphere of mass $m$ rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed $\mathrm{V}$.

Solution:

$\mathrm{V}=\mathrm{R} \omega$ (Pure rolling)

$\mathrm{K} . \mathrm{E}=\frac{1}{2} I \omega^{2}+\frac{1}{2} m v^{2}$

$\quad \frac{1}{2}\left(\frac{2}{5} m R^{2}\right)\left(\frac{v^{2}}{R^{2}}\right)+\frac{1}{2} m v^{2}$

$\mathrm{~K} . \mathrm{E}=\frac{7}{10} m v^{2}$

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