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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

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

Grade:11

1 Answers

Swapnil Saxena
102 Points
11 years ago

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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