Question

A black hole has an event horizon radius of 4.00×10³ m .

A) What is its mass?

B) Determine the gravitational acceleration it produces at a distance of 4.01×10³ m from its center.

C) Determine the escape speed at a distance of 4.01×10³ m from its center.

Answer 1

Given
Radius of the black hole, R = 4.0 *10^3 m
Part a) The mass of the black hole can be calculated from
the Schwarzschild radius R
                   R = 2 GM / c^2
Here G is the Gravitational constant , G = 6.67 *10^-11 Nm^2/kg^2
And c = 3*10^8 m/s
                    M = (4.0 *10^3 m) ( 3*10^8 m/s)^2 / 2(6.67 *10^-11 Nm^2/kg^2)
                    M = 2.699*10^30 kg
Part b) Distance from the center, r = 4.01 *10^3 m
          Gravitational acceleration, g = GM / r^2
                              g = ((6.67 *10^-11 Nm^2/kg^2)( 2.699 *10^30 kg)/ ( 4.01 *10^3 m)^2
                              g = 11.19 *10^12 m/s^2
Part c) Escape speed , vesc = square root 2 GM / r
                                    = square rooroot ( 2(6.67 *10^-11 Nm^2/kg^2)( 2.699 *10^30 kg)/ ( 4.01 *10^3 m))

Vesc = 2.996 *10^8 m/s

I hope help you !!