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
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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=∫r∞GmMx2dx=−GMmr
Hence, the gravitational potential energy =−GMmr
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