Question

Neutron stars are extremely dense objects formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 13.0 km. Determine the greatest possible angular speed it can have so that the matter at the surface of the star on its equator is just held in orbit by the gravitational force.

Answer 1

Answer:

10989.55932 rad/s

Explanation:

m = Mass of object

M = Mass of neutron star = $2\times 1.989\times 10^{30}\ kg$

R = Radius of neutron star = 13000 m

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

$\omega$ = Angular speed

Here, the gravitational force will balance the centripetal force

$\dfrac{GmM}{R^2}=mR\omega^2\\\Rightarrow \omega=\sqrt{\dfrac{GM}{R^3}}\\\Rightarrow \omega=\sqrt{\dfrac{6.67\times 10^{-11}\times 2\times 1.989\times 10^{30}}{13000^3}}\\\Rightarrow \omega=10989.55932\ rad/s$

The greatest possible angular speed an object can have is 10989.55932 rad/s