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  4. A solid sphere is rolling on a surface as shown in figure, with a translational velocity v ms-1. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is

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Q. A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v\,ms^{-1}$. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen isPhysics Question Image

AIEEEAIEEE 2012System of Particles and Rotational Motion

Solution:

Minimum velocity fin- a body rolling without slipping
$v = \sqrt{\frac{2gh}{1+\frac{K^{2}}{R^{2}}}}$
For solid sphere, $\frac{K^{2}}{R^{2}} = \frac{2}{5}$
$\therefore \quad v = \sqrt{\frac{2gh}{1+\frac{K^{2}}{R^{2}}}} = \sqrt{\frac{10}{7}gh}$