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Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give ##U = \iiint \frac{GM^2}{8 \pi r^4} dv = \frac{-GM^2}{2R}##.

Is my solution correct?

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- Thread starter Ananthan9470
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In summary, the formula for calculating the gravitation energy of a spherical shell is E = -3/5 * (G * M^2 / R). The negative sign in the formula indicates that the energy is always lost or released when the shell is formed. The mass and radius of the shell directly affect its energy, with an increase in mass resulting in an increase in energy and an increase in radius resulting in a decrease in energy. The gravitation energy of a spherical shell is not constant and can change over time. It is also a type of gravitational potential energy and can be converted into other forms, such as kinetic energy, through interactions with other objects.

- #1

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Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give ##U = \iiint \frac{GM^2}{8 \pi r^4} dv = \frac{-GM^2}{2R}##.

Is my solution correct?

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Yes, that looks correct.

The formula for calculating the gravitation energy of a spherical shell is E = -3/5 * (G * M^2 / R), where E is the energy, G is the gravitational constant, M is the mass of the shell, and R is the radius of the shell.

The negative sign in the formula represents the fact that the energy of a spherical shell is always negative. This means that the energy is always released or lost when the shell is formed, as it takes energy to pull the particles of the shell together.

The gravitation energy of a spherical shell is directly proportional to the mass of the shell and inversely proportional to the radius of the shell. This means that as the mass of the shell increases, its energy also increases, while as the radius of the shell increases, its energy decreases.

No, the gravitation energy of a spherical shell is not constant. It depends on the mass and radius of the shell, which can change over time. As the shell attracts more matter or expands, its energy will change accordingly.

The gravitation energy of a spherical shell is a type of gravitational potential energy. It represents the energy that is stored in the gravitational field of the shell and is released when the shell is formed. This energy can also be converted into other forms, such as kinetic energy, when the shell interacts with other objects through gravity.

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