JEE Advance - Physics (2024 - Paper 1 Online - No. 9)
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 ___________.
Answer
12
Explanation
On applying conservation of angular momentum about axis of larger disc.
$$\begin{aligned} & \frac{1}{2} \cdot M\left(\frac{R}{2}\right)^2 \cdot \omega-M\left(\omega^{\prime} R\right) \cdot R-\frac{M R^2}{2} \cdot \omega^{\prime}=0 \\ & \Rightarrow \frac{\omega}{8}=\frac{3 \omega^{\prime}}{2} \\ & \Rightarrow \omega^{\prime}=\frac{\omega}{12} \quad \text { Hence, } \mathrm{n}=12 \end{aligned}$$
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