First slide

Simple hormonic motion

Question

A solid thin metallic disc of radius R is hinged at point O on its rim and freely suspended as shown in the figure. The lower endge of the disc is slightly pulled to the right and released. Then time period of oscillation of the disc is

Difficult

A

$2 π \sqrt{\frac{2 R}{g}}$
B

$2 π \sqrt{\frac{R}{g}}$
C

$2 π \sqrt{\frac{3 R}{2 g}}$
D

$\frac{π}{2} \sqrt{\frac{2 R}{3 g}}$

Solution

$T = 2 π \sqrt{\frac{I_{0}}{{mgr}_{C}}}$
Where $I_{0} =$ moment of inertia of the disc about a horizontal axis through $O = \frac{1}{2} {mR}^{2} + {mR}^{2} = \frac{3}{2} {mR}^{2}$
$r_{C} =$ Distance of centre of mass from the hinge point O = R
$∴ T = 2 π \sqrt{\frac{\frac{3}{2} {mR}^{2}}{mg . R}} = 2 π \sqrt{\frac{3 R}{2 g}}$

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