Mechanics> gravC...

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

Arnab Mandal , 14 Years ago

Grade 11

1 Answers

Swapnil Saxena

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)

Last Activity: 14 Years ago

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Mechanics> gravC...

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

Arnab Mandal , 14 Years ago

Swapnil Saxena

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