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)
$\therefore 10=\sqrt{\frac{\mathrm{R}}{\mathrm{R}^{\prime}}}$
$\Rightarrow R^{\prime}=\frac{R}{100}=\frac{6400}{100}=64 \mathrm{~km}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.