First slide

Rolling motion

Question

A solid sphere and circular disc of same mass and radius are allowed to roll down an inclined plane from the same height without slipping. Find the ratio of times taken by these two to come to the bottom of incline:

Moderate

A

$\sqrt{14} : \sqrt{15}$
B

$15 : 14$
C

$\sqrt{2} : 1$
D

$7 : 9$

Solution

Acceleration of a rolling body on inclined plane is
$a = \frac{g \sin θ}{1 + \frac{k^{2}}{R^{2}}}$
For two bodies time of rolling same length is
$\frac{t_{1}}{t_{2}} = \sqrt{\frac{a_{2}}{a_{1}}} = \sqrt{\frac{1 + \frac{k_{1}^{2}}{R^{2}}}{1 + \frac{k_{2}^{2}}{R^{2}}}}$
For a solid sphere $k_{1}^{2} = \frac{2}{5} R^{2}$
And for disc $k_{2}^{2} = \frac{1}{2} R^{2}$
$\Rightarrow \frac{t_{1}}{t_{2}} = \sqrt{\frac{1 + \frac{2}{5}}{1 + \frac{1}{2}}} = \sqrt{\frac{14}{15}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App