A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.5 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain observed stellar objects called pulsars are believed to belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity ? (Mass of the sun = 2 x ${{10}^{30}}$ kg)
For the object to remain stuck to the star, the gravitational force of the star must be equal to or greater than the centripetal force. Under this condition, the centrifugal force does not overcome the gravitational force and not fly off the object. It means,
Hence for the object to remain stuck, the acceleration due to gravity (g) on the star must be > centripetal acceleration.
