Answer
(a) $7.7\times 10^6Km$
(b) $5.8\times 10^6m/s^2$
(c) decreases by a factor of 2.
Work Step by Step
(a) We can find the required radius as follows:
$R=\frac{2GM}{c^2}$
We plug in the known values to obtain:
$R=\frac{2(6.67\times 10^{-11}Nm^2/Kg^2)(5.2\times 10^{36}Kg)}{(3\times 10^8m/s)^2}$
$R=7.707\times 10^9m$
$\implies R=7.7\times 10^6Km$
(b) We know that
$g=\frac{c^4}{4GM}$
We plug in the known values to obtain:
$g=\frac{(3\times 10^8m/s)^4}{4(6.67\times 10^{-11}N.m^2/Kg^2)(5.2\times 10^{36}Kg)}$
$g=5.8\times 10^6m/s^2$
(c) We know that $g=\frac{c^4}{4GM}$. This equation shows that if the mass of the black hole is doubled, then the acceleration due to the gravity is decreased by a factor of 2.
