Question:
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 ___________.
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 ___________.
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Escape velocity varies as 1/sqrt(R) for fixed mass.
Updated On: Nov 4, 2026
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Correct Answer: 64
Solution and Explanation
\(v_e=\sqrt{\frac{2GM}{R}}\), so for constant mass \(v_e\propto\frac{1}{\sqrt R}\).
\(\frac{v_e'}{v_e}=\sqrt{\frac{R}{R'}}=10\), so \(\frac{R}{R'}=100\).
\(R'=\frac{6400}{100}=64\) km.
Answer: 64
\(\frac{v_e'}{v_e}=\sqrt{\frac{R}{R'}}=10\), so \(\frac{R}{R'}=100\).
\(R'=\frac{6400}{100}=64\) km.
Answer: 64
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