Question

if the distance between two objects is increased four times, then by how many times will the mass of one of the objects be changed to maintain the same gravitational force ?

Answer 1

F = G M m / R²

if

R = 4 R, then F will change. Let us change the mass M to n times of M so that the force remains same.

then

F = G (nM) m / (4 R)²

or

G M m / R² = G (nM) m / 16 R²

n = 16

So, the one of the masses should be changed to 16 times the mass.