1.
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 Fo. 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?

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cryssatemp cryssatemp · Answer 1 · 2019-12-06T18:22:16+01:00

Answer: [tex]F=\frac{3}{4} \frac{GM^{2}}{d^{2}}[/tex]

Explanation:

According to Newton's law of Gravitation for the first case:

[tex]F_{o}=G\frac{(M)(M)}{d^2}=\frac{GM^2}{d^2}[/tex] (1)

Where:

[tex]F_{o}[/tex] is the gravitational force

[tex]G[/tex] is the Gravitational Constant

[tex]M[/tex] is the mass of each container

[tex]d[/tex] is the distance between both containers

Now, for the second case the mass of the first container is [tex]1.5 M[/tex] and the second [tex]0.5 M[/tex]:

[tex]F=G\frac{(1.5 M)(0.5 M)}{d^{2}}[/tex] (2)

Finally:

[tex]F=\frac{3}{4} \frac{GM^{2}}{d^{2}}[/tex]