Physics · Rotational Dynamics

JEE Advanced 2024 — Paper 1 — Question 26

A disc of mass $M$ and radius $R$ is free to rotate about its vertical axis as shown in the figure. $A$ battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass $M$ and radius $R / 2$ is fixed to the motor's thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed $\omega$ . If the angular speed at which the large disc rotates is $\omega / n$ , then the value of $n$ is $\_\_\_\_\_$ .

Question figure

Answer: 12

Numerical answer — enter this value.

Step-by-step solution

Angular momentum about fixed axis remains constant.

$\frac{1}{2} m \frac{R^{2}}{4} \omega-m R^{2} \omega^{\prime}-\frac{1}{2} m R^{2} \omega^{\prime}=0$

$\frac{m R^{2} \omega}{8}=m R^{2} \omega^{\prime}+\frac{1}{2} m R^{2} \omega^{\prime}$

$\frac{\omega}{8}=\frac{3}{2} \omega^{\prime}$

$\frac{\omega}{\omega^{\prime}}=12$

Solution figure

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2024
Paper: Paper 1
Subject: Physics
Chapter: Rotational Dynamics
Topic: Angular Momentum and its Conservation

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