EXPLANATION
Given the Newton’s Law of universal Gravitation:
[tex]F=G\frac{m_1\cdot m_2}{r^2}[/tex]As the force is of 36 N, we can substitute It on the function:
[tex]F=G\frac{m_1\cdot m_2}{r^2}[/tex]If the mass of both objects is doubled, then the force will be stronger by a factor of 4:
[tex]F=G\frac{2m_1\cdot2m_2}{r^2}=G\frac{4m_1m_2}{r^2}[/tex]Also, if the distance between them is doubled, then we will get a factor of 4 as shown as follows:
[tex]F=G\frac{2m_1\cdot2m_2}{(2r)^2}=G\frac{4m_1m_2}{4r^2}[/tex]Then, simplifying both numbers 4, we can conclude that the force will be the same:
[tex]F=G\frac{2m_1\cdot2m_2}{(2r)^2}=G\frac{4m_1m_2}{4r^2}=G\frac{m_1m_2}{r^2}\text{ \lbrack{}Same expression\rbrack}[/tex]
