JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2024
- Hard
- Numerical
Consider a Disc of mass \(5 \mathrm{~kg}\), radius \(2 \mathrm{~m}\), rotating with angular velocity of \(10 \mathrm{rad} / \mathrm{s}\) about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is _______ \(J\).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(250\)
Step-by-step Solution
Detailed explanation
\( \vec{L}_i=I \omega_i=\frac{M R^2}{2} \cdot \omega=100 \mathrm{kgm}^2 / \mathrm{s} \)
\( E_i=\frac{1}{2} \cdot \frac{M R^2}{2} \cdot \omega^2=500 \mathrm{~J} \)
\( \vec{L}_i=\vec{L}_f \Rightarrow 100=2 I \omega_f \)
\( \omega_{\mathrm{f}}=5 \mathrm{rad} / \mathrm{sec} \)
\( E_f=2 \times \frac{1}{2} \cdot \frac{5(2)^2}{2} \cdot(5)^2=250 \mathrm{~J} \)
\( \Delta E=250 \mathrm{~J}\)
\( E_i=\frac{1}{2} \cdot \frac{M R^2}{2} \cdot \omega^2=500 \mathrm{~J} \)
\( \vec{L}_i=\vec{L}_f \Rightarrow 100=2 I \omega_f \)
\( \omega_{\mathrm{f}}=5 \mathrm{rad} / \mathrm{sec} \)
\( E_f=2 \times \frac{1}{2} \cdot \frac{5(2)^2}{2} \cdot(5)^2=250 \mathrm{~J} \)
\( \Delta E=250 \mathrm{~J}\)
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