Question

What happens to the magnitude of the force of gravitation between two objects if – Mass of both objects as well as the distance between them is doubled ?

Answer 1

 Ans: (i) When the mass of either body is doubled, the force is also doubled as per the following equation:         (ii) When the distance between the objects is doubled, the force becomes one fourth of the original force as per the following equation:         Similarly it can be shown that when the distance between the objects is tripled, the force becomes one ninth of the original force.  (iii) In the same way as given in the answer (i) above this can be shown that when the masses of both bodies are doubled, the force becomes four times the original force. 

Answer 2

Heya

Initial case
let mass of bodies are M and m
distance between them is r .
so gravitation force is given by

F = G Mm/r²

now case 2
mass and distance between them is doubled

so new masses are 2M and 2m
and new distance between them is 2r

so

F' = G(2M×2m)/(2r)²
F' = 4GMm/4r²
F' = GMm/r²
so F'=F
no change in force of gravitation.