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

We know,

F = Gm_{1}m_{2}/r^{2}

i)

Suppose m_{1} becomes 2m_{1}:

F^{/} = G(2m_{1})m_{2}/r^{2}

=> F^{/} = 2F

Thus, force is also doubled.

ii)

Suppose r becomes 2r.

F^{//} = Gm_{1}m_{2}/(2r)^{2}

=> F^{//} = F/4

Thus, force becomes one-fourth of original value.

iii)

Suppose both m_{1} and m_{2} are doubled:

F^{///} = G(2m_{1})(2m_{2})/r^{2}

=> F^{///} = 4F

Thus, force becomes four times the original value.

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