The gravitational force between two giant lead spheres is 0.010 N when the centers of the spheres are 20 m apart. What is the distance between their centers when the gravitational force between them is 0.160 N?
From the gravitational equation,
F = G(m1.m2)/r^2, or
F.r^2 = G.m1.m2
Considering the two instances detailed above
F1.r1^2 = F2.r2^2
Substitutinbg values,
0.01*(20)^2 = 0.16*r2^2
4 = 0.16*r2^2
2 = 0.4*r2 (taking square roots)
r2 = 2/0.4 = 20/4 = 5
In the 2nd instance, they are now 5 m apart