Two discs have moments of inertia I1 and I2 about their respective… | JEE Main 2021 (27 Aug, Shift 2)

Q51JEE Main 2021 · 27 AUG · SHIFT 2Medium

Angular Momentum & its Conservation

Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $\omega$ 1 and $\omega$ 2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:

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Answer: (c)

Conservation of $L$ : $\omega = \frac{I_1\omega_1 + I_2\omega_2}{I_1+I_2}$ .
$\Delta K = \frac{1}{2}I_1\omega_1^2 + \frac{1}{2}I_2\omega_2^2 - \frac{(I_1\omega_1+I_2\omega_2)^2}{2(I_1+I_2)}$
Simplifying: $\Delta K = \frac{I_1I_2}{2(I_1+I_2)}(\omega_1-\omega_2)^2$
So the answer is (c).

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