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  4. A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy , (Kr) simultaneously. The ratio Kt: (Kt + Kr) for the sphere is

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Q. A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy , $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is

NEETNEET 2018System of Particles and Rotational Motion

Solution:

$K_{t} = \frac{1}{2} mv^{2}$
$ K_{t} +K_{r} = \frac{1}{2} mv^{2} + \frac{1}{2} I \omega^{2} = \frac{1}{2} mv^{2} + \frac{1}{2} \left(\frac{2}{5} mr^{2}\right)\left(\frac{v}{r}\right)^{2}$
$ = \frac{7}{10} mv^{2} $
So, $\frac{K_{t}}{K_{t} + K_{r} } = \frac{5}{7} $