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The mass of a
star is 1.910×1031 kg and it performs one rotation in 38.50 day. Find
its new period (in days) if the diameter suddenly shrinks to 0.330 times
its present size. Assume a uniform mass distribution before and after.

Angular momentum (L) is conserved and given by
L = Iw
where I is moment of inertia (= (2/5)MR^2 for a sphere)
and w is angular velocity.
w[1] = 2.pi/(38.5 x 24 x 60 x 60) = 1.89 x 10^-6 rad/s
L[2]/L[1] = 1 = I[2]w[2]/(I[1]w[1]
w[2]/w[1] = I[1]/I[2] = R^2/(0.33R)^2 = 9.18
w[2] = 9.18w[1] = 1.74 x 10^-5 rad/s
Period = 2pi/w[2] = 3.61 x 10^5 s