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Two discs of moments of inertia \( I_{1} \) and \( I_{2} \) about their respective axes (normal to the disc and passing …

Q1

Two discs of moments of inertia \( I_{1} \) and \( I_{2} \) about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed \( \omega_{1} \) and \( \omega_{2} \) are brought into contact face to face with their axes of rotation coinciding with each other. What is the loss in kinetic energy of the system in the process?

[JEE Main 2017]

a

\( \frac{I_{1} I_{2}\left(\omega_{1}-\omega_{2}\right)^{2}}{2\left(I_{1}+I_{2}\right)} \)

b

\( \frac{I_{1} I_{2}\left(\omega_{1}-\omega_{2}\right)^{2}}{\left(I_{1}+I_{2}\right)} \)

c

\( \frac{I_{1} I_{2}\left(\omega_{1}+\omega_{2}\right)^{2}}{\left(I_{1}-I_{2}\right)} \)

d

\( \frac{I_{1} I_{2}\left(\omega_{1}+\omega_{2}\right)^{2}}{2\left(I_{1}-I_{2}\right)} \)

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