Question

A proton moving at 0.999 of the speed of light orbits a black hole 3249 km from the center of the attractor. what is the mass of the black hole? a proton moving at 0.999 of the speed of light orbits a black hole 3249 km from the center of the attractor. what is the mass of the black hole? 4.39 × 1030 kg 4.39 × 1036 kg 4.39 × 1033 kg 4.39 × 1025 kg

Answer 1

The mass of the black hole is
`4.39*10^3^3 kg`

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.

`(GMm)/(r^2) =(mv^2)/(r)`

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.

`M=(v^2r)/(G)`

Substitute
`(0.999*3*10^8 m/s)` for v,
`(3249*10^3 m)` for r and
`(6.67*10^-^1^1Nm^2/kg^-^2)` for G.

`M=(v^2r)/(G) \\ =((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`

Therefore, the best option from the given values is
`4.39*10^3^3 kg`