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
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B
=GMmr
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C
=3GMmr
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D
=4GMmr
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Solution

## The correct option is B =−GMmr 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=GmMx2Consider the dW is the small amount of work done in bringing the body without acceleration through the very small distance dxdW=FdxAnd 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=−GMmrHence, the gravitational potential energy =−GMmr

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