When a solid sphere rolls without slipping down an inclined plane making an angle θ with the horizontal, the acceleration of its centre of mass is a. If the same sphere slides without friction, its

Acceleration of the solid sphere when it rolls without slipping down an inclined plane is

a = $\frac{g sinθ}{1 + \frac{I}{{MR}^{2}}}$

For a solid sphere, I = $\frac{2}{5} {MR}^{2}$

a = $\frac{g sinθ}{1 + \frac{2}{5}} = \frac{5}{7} g \sin θ$

Acceleration of the same sphere when it slides without friction down an same inclined plane is

$a^{'} = gsin θ$

Divide (ii) by (i), we get, $\frac{a^{'}}{a} = \frac{7}{5} or a^{'} = \frac{7}{5} a$

When a solid sphere rolls without slipping down an inclined plane making an angle $θ$ with the horizontal, the acceleration of its centre of mass is a. If the same sphere slides without friction, its