Question

Define gravitational potential energy. Derive expression for gravitational potential in the gravitational field of earth at distance r from the centre of the earth.

A
=2GMmr
B
=GMmr
C
=3GMmr
D
=4GMmr
Solution
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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=GmMx2

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=rGmMx2dx=GMmr

Hence, the gravitational potential energy =GMmr

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