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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) root[3/2]Ve
b) 3/2Ve
c) root[2/3]Ve
d) 2/3Ve
The gravitational potential energy of a particle at the center of the earth is -(3/2)(GMm/R)
And that at the surface is (GMm/R)
Since Ve=(2* Gravitational Potential )1/2. Then at Surface it is (2*GM/R)1/2
At the Center it is (2*3/2*GM/R)1/2=(3*GM/R)1/2
Then The ratios of the Escape velocity is Ve1 (at Center)/Ve (at Surface) =(3/2)1/2
So the Correct Option is (A)
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