Question

Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 1.48 m. Two of the spheres have a mass of 2.18 kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces that the spheres exert on each other, what is the magnitude of the initial acceleration of the third sphere?

Answer 1

Add the gravitational forces due to the two spheres at the oppostice corners. The resultant force will be in a direction between them (30 degrees from each).

Get the gravitational force between each pair using Newon's universal equation of gravity,
F = G M1 M2/R^2

The acceleration will be F/m, if the spheres are be themselves floating in space. If they are on a flat horizontal table, the sphere that is free to move will roll and the acceleration rate will be less than the free-space non-rolling case. You need to consider the moment of inertia..

Answer 2

9.8m/s