Explanation:
The gravitational force is given by :
[tex]F=\dfrac{Gm_1m_2}{d^2}[/tex]
Force in option (1) is :
[tex]F_1=\dfrac{Gm^2}{d^2}[/tex]
Force in option (2) is :
[tex]F_2=\dfrac{Gm\times \dfrac{m}{4}}{(\dfrac{d}{2})^2}\\\\F_2=\dfrac{G\times \dfrac{m^2}{4}}{\dfrac{d^2}{4}}\\\\F_2=\dfrac{Gm^2}{d^2}[/tex]
Force in option (3) is :
[tex]F_3=\dfrac{G\times 2m\times 2m}{(2d)^2}\\\\F_3=\dfrac{4Gm^2}{4d^2}\\\\F_3=\dfrac{Gm^2}{d^2}[/tex]
Force in option (4) :
[tex]F_4=\dfrac{G\times \dfrac{m}{4}\times 4m}{d^2}\\\\F_4=\dfrac{Gm^2}{d^2}[/tex]
It is clear that in all the cases the force of gravitation is the same.
