A solid sphere is in pure rolling motion. In rolling motion, a body possesses translational kinetic energy $(K_{t})$ as well as rotational kinetic energy $(K_{r})$ simultaneously. The ratio of $K_{t}$ and $K_{r}$ for the sphere is

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10:7

5:2

7:1

2:5

answer is B.

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Detailed Solution

$K_{t} = \frac{1}{2} m v^{2} And K_{r} = \frac{1}{2} l ω^{2} = \frac{1}{2} (\frac{2}{5} m r^{2}) {(\frac{v}{r})}^{2} = \frac{1}{5} m v^{2} ∴ \frac{K_{t}}{K_{r}} = \frac{\frac{1}{2} m v^{2}}{\frac{1}{5} m v^{2}} = \frac{5}{2}$

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