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 7870 N . They plan to accomplish this by placing a mini black hole 5.23 × 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

Answer:

43850.49112 kg

Explanation:

M = Mass of moon = $7.36\times 10^{22}\ kg$

r = Distance from Moon's center = $5.23\times 10^6\ m$

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

m = Mass of black hole

F = Force = 7870 N

From the universal force of gravity we have

$F=\frac{GMm}{r^2}\\\Rightarrow m=\frac{Fr^2}{GM}\\\Rightarrow m=\frac{7870\times (5.23\times 10^6)^2}{6.67\times 10^{-11}\times 7.36\times 10^{22}}\\\Rightarrow m=43850.49112\ kg$

The mass of the mini black hole is 43850.49112 kg