Question

Certain neutron stars (extremely dense stars) are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, what must be its minimum mass so that material on its surface remains in place during the revis's rotation?

Answer 1

Answer:

Mass, $M=4.73\times 10^{24}\ kg$

Explanation:

It is given that,

Angular velocity of the neutron stars, $\omega=1\ rev/s=6.28\ rad/s$

Radius of the star, r = 20 km = 20000 m

Let M is the mass of the star. The magnitude of acceleration due to gravity is balanced by the centripetal acceleration of the stars.

$\dfrac{GM}{r^2}=\omega^2r$

$M=\dfrac{\omega^2r^3}{G}$

$M=\dfrac{(6.28)^2\times (20000)^3}{6.67\times 10^{-11}}$

$M=4.73\times 10^{24}\ kg$

So, the minimum mass so that material on its surface remains in place during the revis's rotation is $4.73\times 10^{24}\ kg$. Hence, this is the required solution.