Question

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 gravitational force it would experience would be the same from both rings?

• A. A
• B. B
• C. C
• D. D

Hint:

The gravitational force due to a ring of mass decreases with the square of the distance from the center. The forces balance when the mass is at the appropriate distance from both rings.

Answer 1

The Correct Option is B

The gravitational force on a point due to a ring of mass is given by the formula: \[ F = \frac{GMm}{r^2} \] where \( G \) is the gravitational constant, \( M \) is the total mass of the ring, \( m \) is the mass experiencing the force, and \( r \) is the distance from the center of the ring to the mass. To find the position where the forces from both rings are equal, we equate the gravitational forces from both rings.
The forces from the rings at positions A, B, C, and D need to balance.
By symmetry and considering the relative distances, position B is the location where the forces from both rings are equal.
Thus, the correct answer is (b).