Answer:
the mass of the neutron stars is 2.02 × 10₂₅kg
Explanation:
The neutron stars rotate in the orbit of radius 40km
The centripetal force that acts on the neutron star is
[tex]F_c = \frac{mv^2}{r}[/tex]
The gravitational force between the neutron stars and the earth is
[tex]F_G= \frac{GMm}{r^2}[/tex]
[tex]F_G = F_c[/tex]
[tex]\frac{GMm}{r^2} = \frac{mv^2}{r} \\\\\frac{GM}{r} = v^2[/tex]
For a circular rotating object , the relation between the linear velocity and angular velocity is
[tex]v = r \omega[/tex]
substitute [tex]r\omega[/tex] for v in equation [tex]\frac{GM}{r} = v^2[/tex] ans solve for M
[tex]\frac{GM}{r} = v^2\\\\\frac{GM}{r} =(r\omega)^2\\\\M = \frac{r^3\omega^2}{G}[/tex]
angular velocity, [tex]\omega[/tex] = 0.73rev/sec = 4.587rad/sec
The distance from the neutron stars to the centre of the earth is
r = 40km = 40 × 10³m
gravitational constant, G =6.67 × 10⁻¹¹Nm²/kg²
Calculate the mass of neutron star by using the equation [tex]M = \frac{r^3\omega^2}{G}[/tex]
[tex]M = \frac{(40\times10^3)(4.587)^2}{6.67\times10^-^1^1} \\\\M = 2.02\times10^2^5kg[/tex]
Therefore, the mass of the neutron stars is 2.02 × 10₂₅kg
