Gravitational Potential of a Spherical Shell
The Gravitational Potential of a Spherical Shell is calculated using the Gravitational Potential formula,
Now for calculating the Gravitational Potential of a Spherical Shell consider a thin uniform spherical shell of the radius (R) and mass (M), then
Case 1: At point ‘P’ which is inside the spherical shell such that r<R.
V is a constant as E = 0 and the gravitational potential is given by,
V = -GM/R
Case 2: At point ‘P’ which is at the surface of the spherical shell such that r = R.
we know that, E = -GM/R2.
Now,
V = –
solving the integral from (0 to R), we get, Gravitational Potential as
V = -GM/R
Case 3: At point ‘P’ which is outside the spherical shell such that r>R
We know that E = -GM/r2.
Now,
V = –
solving the integral from (0 to r), we get, Gravitational Potential as
V = -GM/r
Gravitational Potential Energy
The energy possessed by objects due to changes in their position in a gravitational field is called Gravitational Potential Energy. It is the energy of the object due to the gravitational forces. The work done per unit mass to bring the body from infinity to a location inside the gravitational field of any object is known as gravitational potential and the energy change here is called Gravitational Potential Energy. Let’s learn about Gravitational Potential Energy in detail in this article.
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