Answer:
It would shrink to a radius of 2.95 km
Explanation:
In order to be a black hole, the Sun must shrink so that its radius becomes equal to its Schwarzschild radius:
[tex]r=\frac{2GM}{c^2}[/tex]
where
G is the gravitational constant
[tex]M=1.99\cdot 10^{30} kg[/tex] is the mass of the Sun
c is the speed of light
Substituting into the equation, we find
[tex]r=\frac{2(6.67\cdot 10^{-11}m^3 kg^{-1} s^{-2})(1.99\cdot 10^{30} kg)}{(3\cdot 10^8 m/s)^2}=2950 m=2.95 km[/tex]
So, the Sun should shrink to a radius of 2.95 km.
