Q.

The radius in kilometer to which the present radius of earth R=6400 km to be compressed so that the escape velocity is increased 10 times is

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answer is 64.

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Detailed Solution

Escape velocity ve=2GMR⇒ve ∝1R ⇒v1v2=R2R1 ⇒v10v=R2R⇒1100=R2R⇒R2=R100=6400100=64 km
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The radius in kilometer to which the present radius of earth R=6400 km to be compressed so that the escape velocity is increased 10 times is