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 Re = 4 Rm, ge = 6gm;
\( \Rightarrow \frac{{{V_m}}}{{{V_e}}} = \frac{{\sqrt {2{g_m}{R_m}} }}{{\sqrt {2{g_e}{R_e}} }}\)
\( = \sqrt {\frac{{{g_m}{R_m}}}{{6{g_m} \times 4{R_m}}}} = \sqrt {\frac{1}{{24}}} = 0.204\)
Vm = 0.204 Ve;