Explanation:
Given that,
The mass of an object, m = 1 kg
The mass of Earth, [tex]m_e=6\times 10^{22}\ kg[/tex]
The mass of Moon, [tex]m_m=7.4\times 10^{22}\ kg[/tex]
The distance between the two bodies, [tex]d=3.8\times 10^5\ km =3.8\times 10^8\ m[/tex]
The gravitational force between the object and the earth,
[tex]F=\dfrac{Gmm_e}{d^2}\\\\=\dfrac{6.67\times 10^{-11}\times 1\times 6\times 10^{22}}{(3.8\times 10^8)^2}\\\\=2.77\times 10^{-5}\ N[/tex]
The gravitational force between the object and the Moon,
[tex]F=\dfrac{Gmm_m}{d^2}\\\\=\dfrac{6.67\times 10^{-11}\times 1\times 7.4\times 10^{22}}{(3.8\times 10^8)^2}\\\\=3.41\times 10^{-5}\ N[/tex]
Hence, this is the required solution.
