To Find :
The acceleration of the heavier object.
Solution :
Force of gravitation on lighter object by heavier object is :
[tex]F = \dfrac{Gm(4m)}{100^2}[/tex]
Acceleration of lighter object is given by :
[tex]a_s = \dfrac{4Gm}{100^2}\\\\m = \dfrac{50^2}{G}[/tex] .....1)
Now, acceleration of heavier object when separation between them is 25 km :
[tex]4ma_h = \dfrac{Gm(4m)}{25}\\\\a_h = \dfrac{Gm}{25}[/tex].....2)
Putting value of m in equation 2, we get :
[tex]a_h = \dfrac{G\times 50^2}{G \times 25}\\\\a_h = \dfrac{2500}{25}\\\\a_h = 100\ m/s^2[/tex]
Therefore, the acceleration of the heavier object is 100 m/s².