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JEE Main 2021 (17 Mar, Shift 1) · Escape Velocity

Escape Velocity question from JEE Main 2021 (17 Mar, Shift 1)

Q47JEE Main 2021 · 17 MAR · SHIFT 1Medium

Escape Velocity

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 ___________.

Numerical answer type. Work it out, then open the answer.

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Answer: 64

For the same mass, $v_e = \sqrt{\frac{2GM}{R}} \propto \frac{1}{\sqrt{R}}$ .
$v_e' = 10v_e \Rightarrow R' = \frac{R}{100}$ .
$R' = \frac{6400}{100} = 64$ km.
Answer: $64$ km.

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