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Certain neutron stars (extremely dense stars) are believed to be rotating at about 14 revs/s.
If such a star has a radius of 25 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

Answer :

boffeemadrid

Answer:

[tex]1.81263\times 10^{27}\ kg[/tex]

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

M = Mass of the star

m = Mass of object at a distance r

r = Radius = 25 km

N = 14 rev/s

The gravitational force of will balance the centripetal acceleration

[tex]\dfrac{GMm}{r^2}=\dfrac{mv^2}{r}[/tex]

Velocity is given by

[tex]v=r\omega[/tex]

[tex]\dfrac{GMm}{r^2}=\dfrac{mr^2\omega^2}{r}\\\Rightarrow M=\dfrac{r^3\omega^2}{G}\\\Rightarrow M=\dfrac{25000^3\times (14\times 2\pi)^2}{6.67\times 10^{-11}}\\\Rightarrow M=1.81263\times 10^{27}\ kg[/tex]

The mass of the neutron star is [tex]1.81263\times 10^{27}\ kg[/tex]

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