Gravitational Potential of a Uniform Solid Sphere
The Gravitational Potential of a uniform solid sphere can easily be calculated using the gravitational potential formula. Let’s consider a thin uniform solid sphere of the radius (R) and mass (M) then,
Case 1: At point ‘P’ which is inside the solid sphere such that r<R, the gravitational potential is given by,
E = -GMr/R3
Now,
V = –
Integrating over the limit from (0 to r)
Now the Gravitational Potential is given by,
V = -GM [(3R2 – r2)/2R2]
Case 2: At point ‘P’ at the surface of the solid sphere such that r = R
E = -GM/R2
V = –
Integrating over the limit from (0 to r)
V = -GM/R
Case 3: At point ‘P’ outside the solid sphere such that r > R
V = -GM/R
Case 4: At the centre of the solid sphere gravitational potential is given by,
V =(-3/2) × (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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