Gravitation Question 160
Question: The ratio of the radii of planets A and B is $ [k_{1}] $ and ratio of acceleration due to gravity on them is $ [k_{2}] $ . The ratio of escape velocities from them will be [BHU 2002]
Options:
A) $ [k_{1}k_{2}] $
B) $ [\sqrt{k_{1}k_{2}}] $
C) $ [\sqrt{\frac{k_{1}}{k_{2}}}] $
D) $ [\sqrt{\frac{k_{2}}{k_{1}}}] $
Show Answer
Answer:
Correct Answer: B
Solution:
$ [v=\sqrt{2gR}] $ Þ $ [\frac{v_{A}}{v_{B}}=\sqrt{\frac{g_{A}}{g_{B}}\times \frac{R_{A}}{R_{B}}}=\sqrt{k_{1}\times k_{2}}=\sqrt{k_{1}k_{2}}] $
