First slide

Applications of SHM

Question

A number of holes are drilled along a diameter of a disc of radius R. To get minimum time period of oscillations, the disc should be suspended from a horizontal axis passing through a hole whose distance from the centre should be

Difficult

A

$\frac{R}{2}$
B

$\frac{R}{\sqrt{2}}$
C

$\frac{R}{2 \sqrt{2}}$
D

$z e r o$

Solution

Distance of hinge point from center of disc is let say $l$ .
$T = 2 π \sqrt{\frac{L}{g}} where L = \frac{l^{2} + k^{2}}{l}$
$\begin{array}{l} Here k^{2} = \frac{R^{2}}{2} \\ ∴ L = \frac{l^{2} + \frac{R^{2}}{2}}{l} = l + \frac{R^{2}}{2 l} \end{array}$
For minimum time period, L should be minimum. Hence $\frac{d L}{d l} = 0$
$\begin{array}{l} \Rightarrow \frac{d}{d l} (l + \frac{R^{2}}{2 l}) = 0 \\ \Rightarrow 1 + \frac{R^{2}}{2} (\frac{- 1}{l^{2}}) = 1 - \frac{R^{2}}{2 l^{2}} = 0 \\ \Rightarrow l = \frac{R}{\sqrt{2}} \end{array}$

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