Answer:
43850.49112 kg
Explanation:
M = Mass of moon = [tex]7.36\times 10^{22}\ kg[/tex]
r = Distance from Moon's center = [tex]5.23\times 10^6\ m[/tex]
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
[tex]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[/tex]
The mass of the mini black hole is 43850.49112 kg