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  4. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω1 and ω2 . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:-

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Q. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$ . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:-

NEETNEET 2017System of Particles and Rotational Motion

Solution:

$\Delta KE =\frac{1}{2} \frac{I_{1} I_{2}}{I_{1}+I_{2}}\left(\omega_{1}-\omega_{2}\right)^{2}$
$=\frac{1}{2} \frac{I^{2}}{(2 I)}\left(\omega_{1}-\omega_{2}\right)^{2}$
$=\frac{1}{4} l\left(\omega_{1}-\omega_{2}\right)^{2}$