Answer:
[tex]4.5\ \text{N}[/tex]
Explanation:
[tex]F_1[/tex] = Gravitational force between the objects = [tex]18\ \text{N}[/tex]
[tex]r_1[/tex] = Initial distance between the two objects
[tex]r_2[/tex] = Final distance between the two objects = [tex]2r_1[/tex]
Gravitational force between two objects is given by
[tex]F=\dfrac{Gm_1m_2}{r^2}[/tex]
So
[tex]F\propto \dfrac{1}{r^2}[/tex]
[tex]\dfrac{F_2}{F_1}=\dfrac{r_1^2}{r_2^2}\\\Rightarrow \dfrac{F_2}{F_1}=\dfrac{r_1^2}{(2r_1)^2}\\\Rightarrow \dfrac{F_2}{F_1}=\dfrac{1}{4}\\\Rightarrow F_2=\dfrac{F_1}{4}\\\Rightarrow F_2=\dfrac{18}{4}\\\Rightarrow F_2=4.5\ \text{N}[/tex]
The new force of attraction between the objects is [tex]4.5\ \text{N}[/tex].
