Q85 / 90 · JEE Main 2021 (17 Mar Shift 1) · Physics

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 _______.

Correct answer: 64

Solution

$V_{e} = \sqrt{\frac{2 G m}{R}} \dots (1)$

$10 V_{e} = \sqrt{\frac{2 G m}{R^{'}}} \dots (2)$

$∴ 10 = \sqrt{{\frac{R}{R}}^{'}}$

$\Rightarrow R^{'} = \frac{R}{100} = \frac{6400}{100} = 64 km$

Hence, the correct answer is 64.

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