Question

Earth has 4 times the radius of moon and 6 times the acceleration due to gravity on moon. Then the escape velocity for moon is 
1. 4.89 times the escape velocity of earth
2. 0.204 times the escape velocity of earth
3. 2.45 times the escape velocity of earth
4. 0.408 times the escape velocity of earth

Answer 1

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;