Question

Certain neutron stars (extremely dense stars) are believed to be rotating at about 0.76 rev/s. If such a star has a radius of 10 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

i got 3.4187*10^23 but its not right?

Answer 1

Assuming that gravity is the main force holding the neutron star together, require that the surface centripetal acceleration, R w^2, be less than the acceleration of gravity, GM/R^2.

w is the angular rotation velocity,
2 pi x 0.76 = 4.78 rad/s

G is the universal constant of gravity.
Solve for the minimum M, when
G M/R^2 = R w^2

M = R^3 w^2/G

There may be additional "strong" neutron-neutron forces also holding the star together, so I am not sure this problem makes sense.