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A circular disk of moment of inertia \( I_{t} \) is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed \( \omega_{i} \). Another disk of moment of inertia \( I_{b} \) is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed \( \omega_{f} \). The energy lost by the initially rotating disc to friction is
[CBSE PMT 2010]
(a) \( \frac{1}{2} \frac{I_{b} I_{t}}{\left(I_{t}+I_{b}\right)} \omega_{i}^{2} \)
(b) \( \frac{1}{2} \frac{I_{b}{ }^{2}}{\left(I_{t}+I_{b}\right)} \omega_{i}{ }^{2} \)
(c) \( \frac{1}{2} \frac{I_{t}{ }^{2}}{\left(I_{t}+I_{b}\right)} \omega_{i}^{2} \)
(d) \( \frac{I_{b}-I_{t}}{\left(I_{t}+I_{b}\right)} \omega_{i}{ }^{2} \)
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