Gravitation Question 357
Question: The acceleration due to gravity on the surface of the moon is 1/6 that on the surface of earth and the diameter of the moon is one-fourth that of earth. The ratio of escape velocities on earth and moon will be
Options:
A) $ [\frac{\sqrt{6}}{2}] $
B) $ [\sqrt{24}] $
C) 3
D) $ [\frac{\sqrt{3}}{2}] $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ [v_{e}=\sqrt{2g_{e}R_{e}};=v_{m}=\sqrt{2g_{m}R_{m}}] $ $ [\frac{v_{e}}{v_{m}}=\sqrt{\frac{g_{e}}{g_{m}}\frac{{R_{e}}}{R_{m}}}=\sqrt{\frac{g_{e}}{g_{e}/6}\frac{{R_{e}}}{{R_{e}}/4}}=\sqrt{24}] $
