Question

In what ratio the mass 4m should be split so the value of gravitational force comes maximum for a fix distance d between the masses?
F=G(4m-x)/r^2 G/r^2(4m-x^2)

Answer 1

Let mass 4m be Z 
F=G(m1*(Z-m1)/d^2 
Using calculus... 
dF/dm1=0=G(Z-m1)/d^2 -m1/d^2) 

solving for m1, 
Z-m1-m1=0 
m1=Z/2 

So split into 2m, and2m. 

Now if you don't know the wonderful world of calculus, then plot the following parabola, and see where it is max: 
F=G(m1*(Z-m1)/d^2 
k=Z(m1)-(m1)^2