How many times will the force of gravitational attraction between two balls change if the mass

How many times will the force of gravitational attraction between two balls change if the mass of one of them is doubled, the mass of the other is increased by three times, and the distance between the centers of the balls is halved?

The force of gravitational attraction between two balls having masses m₀₁ and m₀₂ kg and the distance between the centers of the balls R₀ meters can be determined by the law of universal gravitation F₀ = G ∙ m₀₁ ∙ m₀₂ / R₀ ^ 2, where the coefficient G = 6.67 ∙ 10 ^ ( – 11) N ∙ m ^ 2 / kg ^ 2 – gravitational constant.

If the mass of one of the balls is doubled m₁ = 2 ∙ m₀₁, the mass of the other is increased by three times m₂ = 3 ∙ m₀₂, and the distance between the centers of the balls is halved R = R₀ / 2, then the force of gravitational attraction between the two balls will become:

F = G ∙ m₁ ∙ m₂ / R ^ 2 or

F = G ∙ 2 ∙ m₀₁ ∙ 3 ∙ m₀₂ / (R₀ / 2) ^ 2;

F = G ∙ 24 ∙ m₀₁ ∙ m₀₂ / R₀ ^ 2.

To determine how many times it will change, we find the ratio:

F / F₀ = (G ∙ 24 ∙ m₀₁ ∙ m₀₂ / R₀ ^ 2) / (G ∙ m₀₁ ∙ m₀₂ / R₀ ^ 2);

F / F₀ = 24.

Answer: the force of gravitational attraction between two balls will increase by 24 times.