Two discs A and B are mounted coaxially on a vertical axle. The dis...

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Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and \( 2 \mathrm{I} \) respectively about the common axis. Disc \( \mathrm{A} \) is imparted an initial angular velocity \( 2 \omega \) using the entire potential energy of a spring compressed by a distance \( x_{1} \). Disc \( B \) is imparted an angular velocity \( \omega \) by a
\( \mathrm{P} \) spring having the same spring constant and compressed by a distance \( \mathrm{x}_{2} \). Both the discs rotate in the

W clockwise direction. When disc \( \mathrm{B} \) is brought in contact with \( \operatorname{disc} \mathrm{A} \), they acquire a common angular velocity in time t.
The loss of kinetic energy the above process is
(A) \( \frac{\mathrm{I} \omega^{2}}{2} \)
(B) \( \frac{\mathrm{I} \omega^{2}}{3} \)
(C) \( \frac{\mathrm{I} \omega^{2}}{4} \)
(D) \( \frac{I \omega^{2}}{6} \)
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