Expression for Gravitational Potential Energy at Height (h)
When an object is taken off from the Earth’s surface to a point ‘h’ above the Earth’s surface and the mass of the Earth is taken to be M and the mass of the object is m, such that,
r1 = R
r2 = R +h
Then,
ΔU = GMm/R – GMm/(R+h)
ΔU = GMm [1/R – 1/(R+h)]
ΔU = GMmh/R(R + h)
For a very small value of h R + h >>> h such that, R +h = r and g = GM/R2
On Substituting, we get
ΔU = mgh
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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