Question:

The radius in kilometer to which the present radius of earth $(R=6400 \mathrm{~km})$ to be compressed so that the escape velocity is increased 10 time is

Solution:

$\mathrm{V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}}}$…..(1)

$10 \mathrm{~V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}^{\prime}}} \ldots$ (2)

$\therefore 10=\sqrt{\frac{\mathrm{R}}{\mathrm{R}^{\prime}}}$

$\Rightarrow R^{\prime}=\frac{R}{100}=\frac{6400}{100}=64 \mathrm{~km}$