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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 32×n . The value of n is ____
 

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answer is 2.

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Detailed Solution

Escape velocity, ve=2GMR
Let R be the radius so that escape velocity is increased 10 times
v′=10ve=2GMR′⇒10×2GMR=2GMR′R′=R100=6400100=64km

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