Answered

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Three spheres, with masses indicated above, are
initially far away from each other, and the
gravitational potential energy of the three-sphere
system is zero. The spheres are then brought
together until each sphere is a distance r from
the other two, as shown above. What is the new
gravitational potential energy of the three-sphere
system?

Sagot :

IceShard8

Answer:

-5Gm^2/r

Explanation:

You don't have the graph, but I know what question you are talking about. The answer is above.

The new gravitational potential energy of the three-sphere system will  be[tex]- \frac{5Gm^2}{r}[/tex].

What is gravitational potential energy ?

The energy that an item has due to its location in a gravitational field is known as gravitational potential energy.

For the sphere 1 we have to perform no work. Hence, the work done is zero.

[tex]\rm W_1 = 0[/tex]

The mass m is to be brought to be infinity. Because there is potential at B due to mass m at A point .

[tex]\rm W_2 = \frac{-Gm}{r} \times m \\\\ W_2 =-\frac{Gm^2}{r}[/tex]

The B2 m at C is brought to infinity. For we have to do work . The  gravitational potential energy for the mass 2 m is;

[tex]\rm W_3 = \frac{-Gm}{r} \times 2m\\\\ W_3 = \frac{-4Gm^2}{y} \\\\[/tex]

The new gravitational potential energy of the three-sphere system will be;

[tex]\rm W =W_1+W_2+W_3 \\\\\rm W =-0-\frac{Gm}{r}-4\frac{-Gm^2}{r^2} \\\\ W=\-\frac{-5Gm^2}{r^2}[/tex]

Hence,  the new gravitational potential energy of the three-sphere system will  be[tex]- \frac{5Gm^2}{r}[/tex].

To learn more about the gravitational potential energy, refer;

https://brainly.com/question/3884855

#SPJ2

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