Question

Two discs A and B arc mounted coaxially on a vertical axle. The discs have moments of inertia I and 2l respectively about the common axis. Disc A is imparted an initial angular velocity 2 $\omega$ using the entire potential energy of a spring compressed by a distance $x_1$ Disc B is imparted an angular velocity $\omega$ by a spring having the same spring constant and compressed by a distance $x_1$ Both the discs rotate in the clockwise direction
The ratio of $\frac{x_1}{x_2}$ is

• A. 2
• B. $\frac{1}{2}$
• C. $\sqrt{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (C)

$\sqrt{2}$

$\begin{array}{c}\text{K.E of any disc}=\frac{1}{2}I{\omega }^2\\ \text{P.E of any compressed spring}=\frac{1}{2}K{x}^2\\ \text{Given for 1st disc}\end{array}$

$\begin{array}{c}\frac{1}{2}I(2\omega {)}^2=\frac{1}{2}K{x}_1^2-(1)\\ \text{Given for}2nd\text{disc}\\ \frac{1}{2}2I(\omega {)}^2=\frac{1}{2}k{x}_2^2-(2\end{array}$

$\begin{array}{c}\text{from (1)}6(\to \frac{x_1}{x_2}=\sqrt{2}\\ \text{Hence option}C\text{is correct}\end{array}$