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?

Which of the following would be the correct answer!

The period increases by a factor of eight.
The period is unchanged.
The period decreases to one quarter its normal period.
The period increases by a factor of sixteen.
The period increases by a factor of four.
The period decreases to one half its normal period.
The period decreases to one sixteenth its normal period.
The period increases by a factor of two.
The period decreases to one eighth its normal period.

Thank you for your help.

Explanation / Answer

since no external torques on the star, the angular momentum is conserved angular momentum for a sphere = 2/5 MR^2 w where M, R are the mass and radius of the star and w is the angular velocity 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. Therefore the d. is the correct one.

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