Question

How does gravitational force between two given objects change when the distance between them is doubled?

Answer 1

The gravitational force between the two given objects becomes 1/4th of the original value when the distance between them is doubled.

1. Let the masses of two given objects be M and m, and the distance between them be R.
2. Then, the magnitude of the gravitational force of attraction (F) between them is given by$F=\frac{GMm}{R^2}$.
3. Let the value of the distance between them, after it gets doubled be 2R.
4. The magnitude of the gravitational force of attraction (F') after the distance is doubled, is given by $F\text{'}=\frac{GMm}{{\left(2R\right)}^2}=\frac{GMm}{4R^2}=\frac{F}{4}$
5. Hence, the magnitude of the force of attraction between the two objects becomes 1/4th of the original value.