In the final part of its life cycle a particular rotating spherical star expands

Question

In the final part of its life cycle a particular rotating spherical star expands to four times its normal diameter. Assume the mass remains constant, the mass is uniformly distributed before the expansion and the mass is uniformly distributed after the expansion. How is the period of rotation affected?

Answer choices are :
- period decreases to 1/2 its normal period
- period is unchanged
-period decreases to 1/8 its normal period
-period increases by a factor of 2
-period increases by a factor of 16
-period increases by a factor of 8
-period decreases to 1/16 its normal period
-period increases by a factor of 4

Explanation / Answer

-period decreases to 1/16 its normal period if the radius increases by a factor of four, the moment of inertia (the 2/5 MR^2 term) increases by a factor of 4^2 or 16; in order to conserve angular momentum, the angular velocity must decrease by a factor of 16, which means the period increases by a factor of 16.

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