Gravitation Question 157

Question: If the radius of a planet is R and its density is $ [\rho ] $ , the escape velocity from its surface will be[MP PMT 2001]

Options:

A) $ [v_{e}\propto \rho R] $

B) $ [v_{e}\propto \sqrt{\rho }R] $

C) $ [v_{e}\propto \frac{\sqrt{\rho }}{R}] $

D) $ [v_{e}\propto \frac{1}{\sqrt{\rho }R}] $

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Answer:

Correct Answer: B

Solution:

$ [v_{e}=R\sqrt{\frac{8}{3}G\pi \rho }] $ \ $ [v_{e}\propto R\sqrt{\rho }] $



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