# The ratio of radius of two planets is K and ratio of acceleration due to gravity of both planet is G. What will be the ratio of their escape velocity ?

$(a)\;(KG)^{1/2} \quad (b)\;(KG)^{-1/2} \quad (c)\;(KG)^2 \quad (d)\;{KG}^{-2}$

Escape velocity $v_e= \sqrt {2gR}$
$\large\frac{v_1}{v_2} =\sqrt {\large\frac{g_1}{g_2} \times \frac{R_1}{R_2}}$$=\sqrt {GK} \large\frac{v_1}{v_2}$$=(GK)^{1/2}$
Hence a is the correct answer.
edited Jul 2, 2014