Question

if the distance b/w 2 point masses increases by 2 and a half times, then how does the force b/w them change?

Answer 1

According to Newton's Law of gravitation :
F = Gmm' /r²
F = gravitational force between them
m and m' are the masses of the two bodies .
r is the distance between them .
G is the universal Gravitational constant.
____________
Now the distance between them is increased by 2½ times .
=> r → 2½r
Now Gravitational Force ( F') between them is :
F' = Gmm'/(2½r)²
=(4/25)× (Gmm'/r² )
=> F' = 4/25 F
new Gravitational force ( F') reduced by 4/25 times then the initial ( F),
______________
hope it helps !

Answer 2

Answer:

the decrease in gravitational attraction is not a linear one. The force of gravity, as given by Newton's law, is an 'inverse square' law. That means that the force of gravity is inversely proportional to the square of the distance between the centers of mass. So

F α 1 / r^2

So, if the distance doubles, the force or gravity falls by 1/4.

If the distance trebles, the force fall be 1/9 and so on.