Answer:
[tex]1.98\cdot 10^{20}N[/tex]
Explanation:
The tension in the cable would be exactly equal to the force of gravity between Moon and Earth, which is given by:
[tex]F=G \frac{mM}{r^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
[tex]m=7.35\cdot 10^{22} kg[/tex] is the mass of the Moon
[tex]M=5.97\cdot 10^{24} kg[/tex] is the mass of the Earth
[tex]r=3.84\cdot 10^8 m[/tex] is the distance between Moon and Earth
Substituting numbers into the equation, we find
[tex]F=(6.67\cdot 10^{-11}) \frac{(7.35\cdot 10^{22})(5.97\cdot 10^{24})}{(3.84\cdot 10^8)^2}=1.98\cdot 10^{20}N[/tex]
