Two masses are separated by a distance r. If this distance is doubled, is the force of interaction between the two masses doubled, halved, or changed by some other amount? explain

Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

This is mathematically represented as

F = (G X m1 x m2) / r∧2

where F is the force acting between the charged particles

r is the distance between the two charges measured in m

G is the gravitational constant which has a value of 6.674*10^-11 Nm^2 kg^-2

m1 and m2 are the masses of the objects measured in Kg

Now if the distance between the is doubled then r becomes 2r. Substituting this in the above formula we get the new Force as

Force (new) = (G X m1 x m2) / (2r) ∧2

Thus dividing Force (new) / Force we get

Force (new) / Force = 1/4.

Thus the gravitational force becomes 1/4th of the original value if the distance between the two masses are doubled.

If the interaction is gravitational or electrical, it gets multiplied by (1/2-squared) or 1/4.