A) 5.6 km/s
B) 11.2 km/s
C) 22.4 km/s
D) 44.8 km/s
Correct Answer: C
Solution :
Given: Escape velocity of a body \[({{v}_{e}})=11.2\] km/s. New mass of the earth \[{{M}_{e}}=2{{M}_{e}}\] and new radius of the earth\[({{R}_{e}})=0.5\,{{R}_{e}}.\] We know that escape velocity\[({{v}_{e}})=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}\propto \sqrt{\frac{{{M}_{e}}}{{{R}_{e}}}}.\] Therefore\[\frac{{{v}_{e}}}{{{v}_{e}}}=\sqrt{\frac{{{M}_{e}}}{{{R}_{e}}}}=\sqrt{\frac{2\,{{M}_{e}}}{0.5\,{{R}_{e}}}}\] \[=\sqrt{\frac{4\,{{M}_{e}}}{{{R}_{e}}}}=2\sqrt{\frac{{{M}_{e}}}{{{R}_{e}}}}=2{{v}_{e}}=2\times 11.2\] \[=22.4\,\,km\text{/}s\].
You need to login to perform this action.
You will be redirected in
3 sec
