Question

what happens to the gravitational force between two objects if

i) the mass of one object is doubled

ii) distance between two objects is doubled

iii) masses of both the objects are doubled

Answer 1

We know,

F = Gm₁m₂/r²

i)

Suppose m₁ becomes 2m₁:

F^/ = G(2m₁)m₂/r²

=> F^/ = 2F

Thus, force is also doubled.

ii)

Suppose r becomes 2r.

F^// = Gm₁m₂/(2r)²

=> F^// = F/4

Thus, force becomes one-fourth of original value.

iii)

Suppose both m₁ and m₂ are doubled:

F^/// = G(2m₁)(2m₂)/r²

=> F^/// = 4F

Thus, force becomes four times the original value.