Use the diagram below to answer the following questions. 40 spheres of equal mass make two rings of 20 spheres each. The ring on the right has a radius twice as large as the ring on the left.
At what position could a mass be placed so that the net gravitational force that it would experience would be zero?
Show Hint
In problems involving multiple sources of gravitational forces, the net force will be zero where the individual forces are equal and opposite. The distances from the sources must be considered to balance the forces.
In this problem, we have two rings of mass, one with a radius \( r \) and the other with a radius \( 2r \). The gravitational forces from the two rings will cancel each other out at a certain point along the line between the two rings.
To find the point where the net force is zero, we use the principle of superposition, where the force due to each ring will act in opposite directions. The gravitational force due to a ring is proportional to the inverse square of the distance.
At point B, the gravitational forces from both rings are equal in magnitude but opposite in direction, thus cancelling each other out, making the net force zero.
