Answer:
The required angular speed the neutron star is 10992.32 rad/s
Explanation:
Given the data in the question;
mass of the sun M[tex]_S[/tex] = 1.99 × 10³⁰ kg
Mass of the neutron star
M[tex]_N[/tex] = 2( M[tex]_S[/tex] )
M[tex]_N[/tex] = 2( 1.99 × 10³⁰ kg )
M[tex]_N[/tex] = ( 3.98 × 10³⁰ kg )
Radius of neutron star R[tex]_N[/tex] = 13.0 km = 13 × 10³ m
Now, let mass of a small object on the neutron star be m
angular speed be ω[tex]_N[/tex].
During rotational motion, the gravitational force on the object supplies the necessary centripetal force.
GmM[tex]_N[/tex] = / R[tex]_N[/tex]² = mR[tex]_N[/tex]ω[tex]_N[/tex]²
ω[tex]_N[/tex]² = GM[tex]_N[/tex] = / R[tex]_N[/tex]³
ω[tex]_N[/tex] = √(GM[tex]_N[/tex] = / R[tex]_N[/tex]³)
we know that gravitational G = 6.67 × 10⁻¹¹ Nm²/kg²
we substitute
ω[tex]_N[/tex] = √( ( 6.67 × 10⁻¹¹ )( 3.98 × 10³⁰ ) ) / (13 × 10³ )³)
ω[tex]_N[/tex] = √( 2.65466 × 10²⁰ / 2.197 × 10¹²
ω[tex]_N[/tex] = √ 120831133.3636777
ω[tex]_N[/tex] = 10992.32 rad/s
Therefore, The required angular speed the neutron star is 10992.32 rad/s
