Question:

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

Solution:

(64)

$V_{e}=\sqrt{\frac{2 G m}{R}} \quad \cdots$

$10 \mathrm{~V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}^{\prime}}} \quad \cdots$

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

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