1
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Question

# If ve is the escape velocity for earth when a projectile is fired from the surface of earth. Then the escape velocity if the same projectile is fired from its centre is

A
32ve
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B
32ve
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C
23ve
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D
23ve
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Solution

## The correct option is A √32veTo calculate gravitational potential at the center of earth, take a spherical shell element at radius r. dV=−GMr4πr2dr43πR3=−3GMrdrR3Integrating this, we get V=−32GMR The potential at the surface of earth is −GMRSince escape velocity is proportional to the square root of potential energy and hence square root of gravitational potential, escape velocity at centre of earth will be √32ve

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