A) 11 km/sec
B) 22 km/sec
C) 33 km/sec
D) 16.5 km/sec
Correct Answer: B
Solution :
Escape velocity,\[{{v}_{e}}=\sqrt{\frac{2GM}{R}}\] where, \[M=\frac{4}{3}\pi {{4}^{3}}d\] \[\therefore \] \[{{v}_{e}}=\sqrt{\frac{2G\times \frac{4}{3}\pi {{R}^{3}}d}{R}}\] \[{{v}_{e}}=\sqrt{\frac{8\pi {{R}^{2}}d}{3}}\] \[\Rightarrow \] \[{{v}_{e}}\propto R\] Now, \[\frac{{{({{v}_{e}})}_{earth}}}{{{({{v}_{e}})}_{planet}}}=\frac{{{R}_{earth}}}{{{R}_{planet}}}\]
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