Question

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

Answer 1

The gravitational force b/w two bodies having mass M and m and separated by a distance r is denoted as

F = GMm/r2When r is increased by factor 4 , then its effect will be indirectly proportional and in square , means G force will lessened by 16 times ….For compensating this, one of the body needed to be heavier by 16 times

Hence answer is 16

hope it helps u

Answer 2

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