A star `2.5` times the mass of the sun collapsed to a size radius of the `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 steller objects called pulsars are believed to belong this category ). Will an object placed on its equator remain struck to its surface due to gravity ? (Mass of the sun `= 2 xx 10^(30) kg)`.

Explanation

Acceleration due to gravity acting inward is given by
`g = (GM)/(R^(2))`
`= (6.67 xx 10^(-11) xx 2.5 xx 2 xx 10^(30))/((12 xx 10^(3))^(2))`
`= 2.3 xx 10^(12) ms^(-2)`
Centrifugal acceleration is given by
`omega^(2) R = 4pi^(2) v^(2) R = 4 xx ((2)/(7))^(2) xx (1.5)^(2) xx 12,000`
`omega^(2) R = 1.1 xx 10^(6) ms^(-2)`
As the inward force is much greater than the outward centrifugal force at its equator, object will remain stuck and does not fly off due to centrifugal force.