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

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Solution

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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=∫r∞GmMx2dx=−GMmr

Hence, the gravitational potential energy =−GMmr

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