Question

A sphere of mass 255 kg is 18.0 m from a sphere of 895 kg. What is the gravitational force of the mass due to the building? What is the gravitational force of the sphere due to the mass?

Answer 1

1. The gravitational force of the mass due to the building (I assume it is the second sphere) can be found according to the Newton's law of gravity:

$$F_1 = G\dfrac{m_1m_2}{r^2}$$

where $G = 6.67\times 10^{-11}m^3kg^{-1}s^{-2}$ is the gravity constant, $m_1 = 255 kg$, $m_2 = 895kg$ are masses of the spheres, and $r = 18m$ is the distance between the spheres. Thus, obtain:

$$F_1 = 6.67\times 10^{-11}\dfrac{255\cdot 895}{18^2} \approx 4.7\times 10^{-8}N$$

2. The gravitational force of the sphere (I assume the second sphere) due to the first mass is the same (but the direction is opposite), according to the Newton's third law:

$$F_2 = F_1 = 4.7\times 10^{-8}N$$

Answer. $4.7\times 10^{-8}N$, $4.7\times 10^{-8}N$ (in opposite direction).