Speed of Solid Sphere on Inclined Plane – Rankers Physics

Speed of Solid Sphere on Inclined Plane

The speed of a homogenous solid sphere after rolling down an inclined plane of vertical height $h$ from rest without sliding is: (1992)

$\sqrt{\frac{10}{7}gh}$
$\sqrt{gh}$
$\sqrt{\frac{6}{5}gh}$
$\sqrt{\frac{4}{3}gh}$

Solution:

Using conservation of mechanical energy: $mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$. For a solid sphere ($I = \frac{2}{5}MR^2$), solving yields $v = \sqrt{\frac{10}{7}gh}$.

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