First slide

Rolling motion

Question

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

Moderate

A

$\frac{7}{2} a$
B

$\frac{5}{7} a$
C

$\frac{7}{5} a$
D

$\frac{5}{2} a$

Solution

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, $\frac{a^{'}}{a} = \frac{7}{5} or a^{'} = \frac{7}{5} a$

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