Question

Define the term gravitational potential energy. Derive equation of gravitational potential energy of an object of mass,to be raised through a height h from ground

Answer 1

Heya friend,

Here we go :

Gravitational potential energy is defined as the amount of work done in bringing a body from infinity to a given point in the gravitational field of the earth.

When a body lies at infinity from another body, the gravitational force experienced by the body is 0.

Consequently, we can see,

Potential energy of that body is also 0, which is also called 0 level of potential energy.

Derivation :-

Consider earth to be an uniform sphere of radius 'R' and mass 'm' with it's center at O.

We wish to calculate the G.P.E. of a body of mass 'm' at any point 'P' at a distance 'h' from the center of the earth.

Suppose at any instant, before reaching at the point 'P' , the body is at a point 'A' such that OA = x.

Let dw be the small amount of work done in bringing the body from A to any point B.

So,

dw = Fdx

F = $\frac{GMm}{x^{2} }$

So,

W = GMm $[\frac{-1}{x} ]^{r} _{∞}$

   = -GMm [$\frac{1}{r} - \frac{1}{∞}$]

W = G.P.E. = $\frac{-GMm}{r}$

Thanks !

#BAL #answerwithquality

Answer 2

Here is the answer.....

hope it helped u ✌