Thank you for reporting, we will resolve it shortly
Q.
The radius in kilometre, to which the present -ad ins of the earth (R =6400 km) is to be compressed, so that the escape velocity is increased to ten times, is:
EAMCETEAMCET 2003
Solution:
Escape velocity on earth is given by $ {{v}_{es}}=\sqrt{\frac{2GM}{R}} $ $ \frac{{{v}_{e{{s}_{1}}}}}{{{v}_{e{{s}_{2}}}}}=\sqrt{\frac{2GM}{{{R}_{1}}}\times \frac{{{R}_{2}}}{2GM}} $ (Given $ {{v}_{e{{s}_{2}}}}=10{{v}_{e{{s}_{1}}}} $ ) $ \frac{{{v}_{e{{s}_{1}}}}}{{{v}_{e{{s}_{2}}}}}=\sqrt{\frac{{{R}_{2}}}{{{R}_{1}}}} $ $ \frac{{{({{v}_{e{{s}_{1}}}})}^{2}}}{{{(10{{v}_{es}})}^{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}} $ $ \Rightarrow $ $ \frac{1}{100}=\frac{{{R}_{2}}}{{{R}_{1}}} $ or $ {{R}_{2}}=\frac{{{R}_{1}}}{100}=\frac{6400}{100}=64\,km $