Question

The acceleration due to gravity on the surface of moon is $1/6$ that on the earth and the diameter of the earth is $4$ times the diameter of the moon. The rough ratio of the escape velocity of the moon to that of the earth is

• A. $1:4$
• B. $4:1$
• C. $5:1$
• D. $1:5$

Answer 1

The correct option is D $1:5$

Acceleration due to gravity on the surface of a celestial body is given by:

$g=\frac{GM}{R^2}$

It is given that $g_e:g_m=1:6$

and $R_e:R_m=4:1$

Escape velocity for a planet is given by $v=\sqrt{2gR}$

Ratio of escape velocity is given by:

$\frac{v_m}{v_e}=\frac{\sqrt{2g_m{R}_m}}{\sqrt{2g_e{R}_e}}$

$=\frac{1}{\sqrt{6\times 4}}\approx \frac{1}{5}$