Posted by Suroj on Wednesday, January 9, 2013 at 3:40am.
The answer depends upon where the mass is dropped, but since they tell you the moment of inertia of the dropped mass about the axis, that is enough to answer the question.
Angular momentum about the axis is conserved. The original angular velocity of the disc is
w1 = 2 pi/(period1) = 20.9 rad/s
Period is inversely proportional to angyualr velocity
If w2 is the final angular velocity,
I1*w1 = (I1 + I2)*w2
w2 = (0.06/0/10)*w1 = (3/5)*w1
Period2 = (5/3)*w1 = 0.5 seconds
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