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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 ________.
Option: 1 64
Option: 2 45
Option: 3 24
Option: 4 98

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\begin{array}{l} \mathrm{V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}}} \ldots .(1) \\ 10 \mathrm{~V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}^{\prime}}} \ldots(2) \\ \therefore 10=\sqrt{\frac{\mathrm{R}}{\mathrm{R}^{\prime}}} \\ \Rightarrow \mathrm{R}^{\prime}=\frac{\mathrm{R}}{100}=\frac{6400}{100}=64 \mathrm{~km} \end{array}

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