The mass of the black hole is [tex] 4.39*10^3^3 kg [/tex]
The proton moves in a circular orbit of radius r around the black hole with a speed v. The centripetal force required by the proton is provided by the gravitational attractive force between the proton and the black hole.
[tex] \frac{GMm}{r^2} =\frac{mv^2}{r} [/tex]
Here, the mass of the black hole is M, the mass of the proton is m and G is the universal gravitational constant.
Rewrite the expression for M.
[tex] M=\frac{v^2r}{G} [/tex]
Substitute [tex] (0.999*3*10^8 m/s) [/tex] for v, [tex] (3249*10^3 m) [/tex] for r and [tex] (6.67*10^-^1^1Nm^2/kg^-^2) [/tex] for G.
[tex] M=\frac{v^2r}{G} \\ =\frac{(0.999*3*10^8 m/s)^2(3249*10^3 m)}{6.67*10^-^1^1 Nm^2/kg^-^2} \\ =4.375*10^3^3kg [/tex]
Therefore, the best option from the given values is [tex] 4.39*10^3^3 kg [/tex]
