Question

If we consider the gravitational force F between two objects of masses $m_1$ and $m_2$ respectively, separated by a distance R , and we double the distance between them, what is the new magnitude of the gravitational force between them?

• A. F/4
• B. F/2
• C. F
• D. 2F
• E. 4F

Answer 1

The correct option is A F/4

According to Sir Newton's gravitational law the magnitude of gravitational force $F$ between objects of mass $m_1$ and $m_2$ separated by a distance $R$ is given by ,

$F=G\frac{m_1{m}_2}{R^2}$ ............$eq1$ ,

now if the distance between them is doubled i.e. $2R$ ,then the gravitational force will be ,

$F^{\prime }=G\frac{m_1{m}_2}{{\left(2R\right)}^2}=G\frac{m_1{m}_2}{4R^2}$ ,

now by using $eq1$ ,

$F^{\prime }=F/4$