Correct Answer - Option 2 : 0.204 times the escape velocity of earth

__Concept:__

The velocity needed for an object to completely escape the gravity of a large body such as a moon, planet, or star is known as escape velocity.

The escape speed is given by

\({V_e} = \sqrt {\frac{{2GM}}{R}} = \sqrt {2gR} \)

Where R – radius of the planet

g – acceleration due to gravity

__Calculation:__

Given R_{e} = 4 R_{m}, g_{e} = 6g_{m};

\( \Rightarrow \frac{{{V_m}}}{{{V_e}}} = \frac{{\sqrt {2{g_m}{R_m}} }}{{\sqrt {2{g_e}{R_e}} }}\)

\( = \sqrt {\frac{{{g_m}{R_m}}}{{6{g_m} \times 4{R_m}}}} = \sqrt {\frac{1}{{24}}} = 0.204\)

**V**_{m} = 0.204 V_{e};