Question

Two particles are placed at some distance. If the mass of each of the two particles is doubled,

keeping the distance between them unchanged, the value of gravitational force between them will be:​

Answer 1

Given Information,

Two particles of mass (say m) are separated by a distance (say d).

To find :

Gravitational Force if both the masses were to be doubled.

In accordance with Universal Law of Gravitation, force is :

• Directly proportional to the product of masses
• Inversely proportional to the square of distance.

Since, the distance is unchanged, let us only focus on the masses.

$\sf \: F \propto \: {m}^{2}$

If the masses are to be doubled,

$\sf \: F' \propto \: (2m) {}^{2} \\ \\ \implies \sf \: F' = 4 {m}^{2} \\ \\ \implies \boxed{ \boxed{ \sf F' = 4F}}$

Thus, the new force is four times the initial force.