Gravitation Question 353
Question: An asteroid of mass m is approaching earth initially at a distance of$ [10{R_{e}}] $ , with speed$ [v_{i}] $ . It hits the earth with a speed $ [v_{f}({R_{e}},,and,,M_{e}] $ , are radius and mass of earth), then
Options:
A)$ [v_{f}^{2}=v_{i}^{2}+\frac{2GM}{M_{e}R}\left( 1-\frac{1}{10} \right)] $
B) $ [v_{f}^{2}=v_{i}^{2}+\frac{2GM_{e}}{{R_{e}}}\left( 1+\frac{1}{10} \right)] $
C) $ [v_{f}^{2}=v_{i}^{2}+\frac{2GM_{e}}{{R_{e}}}\left( 1-\frac{1}{10} \right)] $
D) $ [v_{f}^{2}=v_{i}^{2}+\frac{2GM}{{R_{e}}}\left( 1-\frac{1}{10} \right)] $
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Answer:
Correct Answer: C
Solution:
-
$ [-\frac{GM_{e}m}{10{R_{e}}}+\frac{1}{2}mv_{i}^{2}=-\frac{GM_{e}m}{{R_{e}}}+\frac{1}{2}mv_{f}^{2}] $
$ [\therefore v_{f}^{2}=v_{i}^{2}+\frac{2GM_{e}}{{R_{e}}}\left( 1-\frac{1}{10} \right)] $ .
