Question

Two containers of water can have their individual masses varied by adding or removing water. The containers are initially a distance d apart, as measured from their centers, and are filled with water so that each has a mass M, as shown in Figure 1 above. The gravitational force that one container exerts on the other is F0. Water is then added to one container so that its mass increases to 1.5M, and water is removed from the other container so that its mass decreases to 0.5M, as shown in Figure 2. What is the new gravitational force exerted on one container by the other?

Answer 1

The initial gravitational force:

$$F_0=\frac{GM^2}{d^2}$$

The new gravitational force exerted on one container by the other:

$$F=\frac{G(0.5M)(1.5M)}{d^2}=0.75\frac{GM^2}{d^2}=0.75F_0$$