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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

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The escape velocity from the Earth's surface is v ....

The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having radius four times that of Earth and the same mass density is:

(1) v                     (2) 2v
(3) 3v                   (4) 4v

Solution

${v_e} = \sqrt {\frac{{2GM}}{R}}  \propto \sqrt {\frac{M}{R}} $

$\therefore {v_e} \propto \sqrt {\frac{{\rho .\frac{4}{3}\pi {R^3}}}{R}} $

$ \therefore {v_e} \propto R$ since mass density $\rho $ is same

$\frac{{{{({v_e})}_{Planet}}}}{{{{({v_e})}_{Earth}}}} = \frac{{{R_{Planet}}}}{{{R_{Earth}}}}$

$ \Rightarrow \frac{{{{({v_e})}_{Planet}}}}{v} = \frac{{4{R_{Earth}}}}{{{R_{Earth}}}} = 4$

$ \therefore {({v_e})_{Planet}} = 4v$

Answer: (4)