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?

5 m.

Explanation:

From newton's law of universal gravitation

F = Gmm'/r² ... Equation 1

Where F = Force between the giant lead spheres, r = distance between the spheres, mm' = product of their mass, G = universal constant.

Making mm' the subject of the equation

mm' = Fr²/G ... Equation 2

Given: F = 0.010 N, r = 20 m

Substitute into equation 2

mm' = 0.010*20²/G

mm' = 4/G.

When the gravitational force between them is 0.16 N,

4/G = 0.16r²/G

Making r² the subject of the equation,

r² = 4/0.16

r² = 25

r = √25

r = 5 m.

Thus the distance is = 5 m.