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Q.

The radius in kilometers to which the present radius of the earth $(R = 6400 km)$ is to be compressed so that the escape velocity is increases to ten times is

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a

6.4

b

64

c

640

d

4800

answer is B.

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Detailed Solution

Escape velocity

V_{e} = \sqrt{2 gR} = \sqrt{\frac{2GM}{R}}

$\frac{V_{1}}{V_{2}} = \sqrt{\frac{R_{2}}{R_{1}}} \Rightarrow \frac{V}{100} = \sqrt{\frac{R_{2}}{6400}}$

$\frac{1}{100} = \frac{R_{2}}{6400}$

$∴ R_{2} = 64 km$

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