First slide

Simple hormonic motion

Question

A uniform square plate of side 'a' is hinged at one of its corners. It is suspended such that it can rotate about horizontal axis. The time period of small oscillation about its equilibrium position.

Moderate

A

$2 π \sqrt{\frac{2 a}{3 g}}$
B

$2 π \sqrt{\frac{\sqrt{2} a}{3 g}}$
C

$2 π \sqrt{\frac{2 \sqrt{2} a}{3 g}}$
D

$2 π \sqrt{\frac{2 \sqrt{2} a}{g}}$

Solution

$T = 2 π \sqrt{\frac{I}{mgd}} = 2 π \sqrt{\frac{m \frac{(a^{2} + a^{2})}{12} + m {(\frac{a}{\sqrt{2}})}^{2}}{mg . \frac{a}{\sqrt{2}}}}$
= $2 π \sqrt{\frac{(\frac{a}{6} + \frac{a}{2}) . \sqrt{2}}{g}} = 2 π \sqrt{\frac{2 \sqrt{2} a}{3 g}}$

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