The force of attraction between balls with masses m1 and m2 placed at a distance R between their centers is F

The force of attraction between balls with masses m1 and m2 placed at a distance R between their centers is F. The force of attraction between balls with masses of 2m1 and 5m2, if the distance between their centers is 2R, is equal to.

Given:

m1, m2 is the mass of two balls;

R is the distance between the centers of two balls;

F1 = F is the force of attraction between the balls;

m3 = 2 * m1, m4 = 5 * m2 – the mass of the balls has been changed;

R2 = 2 * R – the distance between the balls has been changed.

It is required to determine F2 – what will be the force of attraction after changing conditions.

The force of attraction in the first case will be equal to:

F1 = F = G * m1 * m2 / R ^ 2, where G is the gravitational constant.

The force of attraction in the second case will be equal to:

F2 = G * m3 * m4 / R2 ^ 2 = G * 2 * m1 * 5 * m2 / (2 * R) ^ 2 = 10 * G * m1 * m2 / (4 * R ^ 2).

Since F = G * m1 * m2 / R ^ 2, from here we get that:

F2 = 10 * G * m1 * m2 / (4 * R ^ 2) = 10 * F / 4 = 5 * F / 2 = 2.5 * F.

Answer: the force of gravity will be 2.5 * F.