Question

2. The mass of a body is increased by 4 times,
while that of another is increased by 16
times. How should the distance between
them be changed so that the gravitational
force between them remains the same?​

Answer 1

If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.

Answer 2

Answer:

Explanation:

Let F1 be the original force acting between objects when their masses and distance remains the same.

Therefore,

F1 = GM1M2\D^2

Let F2 be the force after the masses of the two objects and distance between them has been changed.

F2 = G×4M1×16M2/D^2

= 64GM1M2/D^2

Given: F1 = F2

Therefore:

GM1M2/D^2 = 64GM1M2/D^2

GM1M2×D^2 = 64GM1M2×D^2

D^2 = 64GM1M2D^2/GM1M2

D^2 = 64D^2

D = root 64D^2

D = 8D

Therefore distance between the two objects increases by 8 times so that the gravitational force between them remains the same.