Question

If the mass of one of two particles is doubled and the distance between them is doubled, the force of attraction between the two particles will

Answer 1

The force of attraction between the two particles will remain the same, because when mass is doubled, force of attraction is doubled. However, when distance between their centers is doubled, then force of  attraction is halved. As such double and half cancel out each other and force of attraction remains the same.

Answer 2

Answer:

The force of attraction between the two particles will become half.

Explanation:

Consider force F between two objects with masses m and m' which are placed r distance apart from each other.

Mass of first object = m

Mass of second object = m'

Distance between the  two objects = r

$F=G\frac{m\times m'}{r^2}$...(1) (Gravitational force)

If the mass of one of two particles is doubled and the distance between them is doubled the force between them be F'.

Mass of first object = m

New mass of second object = M = 2m'

Distance between the  two objects = R = 2r

$F'=G\times \frac{m\time M}{R^2}=\frac{m\times 2m'}{4r^2}=G\frac{m\times m'}{2r^2}$...(2) (Gravitational force)

Dividing (1) from (2):

$\frac{F}{F'}=\frac{G\frac{m\times m'}{r^2}}{G\frac{m\times m'}{2r^2}}$

$F=2F'$

$F'=\frac{F'}{2}$

The force of attraction between the two particles will become half.