A) 6.4
B) 64
C) 640
D) 4800
Correct Answer: B
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 \[{{R}_{2}}=\frac{{{R}_{1}}}{100}=\frac{6400}{100}=64\,km\]
You need to login to perform this action.
You will be redirected in
3 sec
