Answer:
The mass of the mini black hole is 31190.28 kg.
Explanation:
Given that,
The Moon from its orbit around Earth by pulling it with a force of 5910 N, F = 5910 N.
They plan to accomplish this by placing a mini black hole at a distance of [tex]5.09\times 10^6\ m[/tex] from the center of the Moon.
Mass of Moon, [tex]M=7.36\times 10^{22}\ kg[/tex]
We need to find the mass of the mini black hole. There will be gravitational force between moon and the mini black hole. It is given by :
[tex]F=G\dfrac{mM}{r^2}[/tex]
m is mass of black hole
[tex]m=\dfrac{Fr^2}{GM}\\\\m=\dfrac{5910\times (5.09\times 10^6)^2}{6.67\times 10^{-11}\times 7.36\times 10^{22}}\\\\m=31190.28\ kg[/tex]
So, the mass of the mini black hole is 31190.28 kg.
