Gravitation Question 171

Question:A planet has twice the radius but the mean density is $ [\frac{1}{4}th] $ as compared to earth. What is the ratio of escape velocity from earth to that from the planet[MH CET 2004]

Options:

A) 3 : 1

B) 1 : 2

C) 1 : 1

D) 2 : 1

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Answer:

Correct Answer: C

Solution:

$ [v=R\sqrt{\frac{8}{3}\pi \rho G}] $

Þ $ [\frac{v _{p}}{v _{e}}=\frac{R _{p}}{R _{e}}\sqrt{\frac{{{\rho } _{p}}}{{{\rho } _{e}}}}] $ =$ [2\sqrt{\frac{1}{4}}=1] $



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