Question

Derive an expression of gravitational potential energy of a body of mass m located at a distance r from the centre of the earth?

Answer 1

You can refer the pic
-ve sign indicates work done against gravity

Answer 2

The work obtained in bringing a body from infinity to a point in gravitational field is called gravitational potential energy.

Force of attraction between the earth and the object when an object is at the distance a from the center of the earth.

F=  

x  

2

 

GmM

​

 

Consider the dW is the small amount of work done in bringing the body without acceleration through the very small distance dx

dW=Fdx

And total work done to bring the body from infinity to point p which is at distance r from the center of the earth.

w=∫  

∞

r

​

 

x  

2

 

GmM

​

dx=−  

r

GMm

​

 

Hence, the gravitational potential energy =−  

r

GMm

​