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  4. 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 time is .

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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 $10$ time is ________.

JEE MainJEE Main 2021Gravitation

Solution:

$V _{ e }=\sqrt{\frac{2 Gm }{ R }} \ldots$ (1)
$10 V _{ e }=\sqrt{\frac{2 Gm }{ R ^{\prime}}} \ldots$ (2)
$\therefore 10=\sqrt{\frac{ R }{ R ^{\prime}}}$
$\Rightarrow R ^{\prime}=\frac{ R }{100}=\frac{6400}{100}=64\,\,km$