The magnitude of the gravitational force between two particles 0.10m apart is 10N. If the distance between them is increased to 0.20m, calculate the magnitu...

Answer Details

The gravitational force between two particles is given by the formula F = Gm₁m₂/r², where G is the gravitational constant, m₁ and m₂ are the masses of the particles, and r is the distance between them. In this case, the distance between the particles is initially 0.10m and the force is 10N. If the distance is increased to 0.20m, we can use the formula to calculate the new force. Let's assume that the masses of the particles remain constant. The distance between them is doubled, so the new distance is 2r = 0.20m. Plugging this into the formula and solving for the new force, we get: F' = Gm₁m₂/(2r)² = Gm₁m₂/4r² Since the masses of the particles and the gravitational constant are constants, the only thing that has changed is the distance between the particles. Therefore, the new force is proportional to 1/r². Since r has doubled, the new force will be (1/2)² = 1/4 of the original force. So, the new force is: F' = (1/4)F = (1/4)10N = 2.5N Therefore, the magnitude of the new force is 2.5N. Option (C) is the correct answer.