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QJEEM24Ph1e19: JEE Main 2024 Physics - Class 11 JEEM24Ph1e19 Solution: Consider a Disc of mass , radius , rotating with angular…

JEE Main 2024 (Online) 30th January Morning Shift Physics - Rotational Motion Question 21 English

Consider a Disc of mass 5 kg5 \mathrm{~kg} , radius 2 m2 \mathrm{~m} , rotating with angular velocity of 10 rad/s10 \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.

Step-by-Step Verified Solution

amp;L⃗i=Iωi=MR22⋅ω=100 kgm2/samp;Ei=12⋅MR22⋅ω2=500 Jamp;L⃗i=L⃗f⇒100=2Iωfamp;ωf=5 rad/secamp;Ef=2×12⋅5(2)22⋅(5)2=250 Jamp;ΔE=250 J\begin{aligned}& \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_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}\end{aligned}

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