Question

The evil team of Ms. Moonstruck and Mr. Luny intend to deflect the Moon from its orbit around Earth by pulling it with a force of 5910 N . They plan to accomplish this by placing a mini black hole 5.09 × 10 6 m from the center of the Moon and letting gravitation do what gravitation does. What must the mass of the mini black hole be for the evil duo's evil scheme to succeed? The mass of the Moon is 7.36 × 10 22 kg .

Answer 1

The mass of the mini black hole is 31190.28 kg.

Step-by-step 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
`5.09* 10^6\ m` from the center of the Moon.

Mass of Moon,
`M=7.36* 10^(22)\ kg`

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 :

`F=G(mM)/(r^2)`

m is mass of black hole

`m=(Fr^2)/(GM)\\\\m=(5910* (5.09* 10^6)^2)/(6.67* 10^(-11)* 7.36* 10^(22))\\\\m=31190.28\ kg`

So, the mass of the mini black hole is 31190.28 kg.