Neutron stars — UPSC CSE 2001 Physics PYQ

A star of the size of our sun having a radius of 7 \times 10^5\text{ km} and having a mass 2 times as that of the sun is rotating at a speed of one revolution every 10 days. If the star undergoes a gravitational collapse to a neutron star of radius 10\text{ kms}, assuming that the star is a uniform sphere at all times, calculate the rotation speed of the neutron star. The moment of inertia of solid about its diameter is 2/5\text{ MR}^2 where M and R are the mass and radius of the solid sphere respectively.