Question

The gravitational force between two objects is 2N. What will be the gravitational force between them if the distance between them is doubled

Answer 1

Dear Student,
Let the two bodies are having mass M₁ and M₂ and distance between them is d then the gravitational force acting between them is given by the equation-
Gravitational force = $F=\frac{G{M}_1{M}_2}{d^2}$=2N
Now if the distance between them is doubled = 2d then gravitational force-
$$\begin{gathered} F\text{'}=\frac{G{M}_1{M}_2}{{\left(2d\right)}^2} \\ F\text{'}=\frac{G{M}_1{M}_2}{4d^2} \\ F\text{'}=\frac{F}{4} \\ F\text{'}=\frac{2N}{4}=\frac{N}{2} \end{gathered}$$
Thus if the distance between them is doubled the force will become N/2.
Regards.