First slide

Surface tension

Question

A thin spherical shell is rolling without slipping on a horizontal surface. If $K_{R} and K_{T}$ respectively represent kinetic energy due to rotational motion and kinetic energy due to translational motion, then $\frac{K_{R}}{K_{T}}$ is

Easy

A

$\frac{3}{4}$
B

$\frac{2}{3}$
C

$\frac{3}{5}$
D

$\frac{2}{5}$

Solution

$K_{R} = \frac{1}{2} (\frac{2}{3} m R^{2}) {(\frac{V}{R})}^{2} = \frac{1}{3} m V^{2}$
and $K_{T} = \frac{1}{2} m V^{2}$
$∴ \frac{K_{R}}{K_{T}} = \frac{\frac{1}{3} m V^{2}}{\frac{1}{2} m V^{2}} = \frac{2}{3}$

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