There are two planets. The ratio of radius of two planets is `k` but ratio of acceleration due to gravity of both planets is g. What will be the ratio of their escape velocity ?

Options

A. `(Kg)^(1//2)`
B. `(Kg)^(-1//2)`
C. `(Kg)^2)`
D. `(Kg)^(-2)`

Answer

A

Explanation

Given `R_1/R_2 = K ` and ` g_1/g_2 =g `
Escape velocity , ` v_e = sqrt(2gR)`
` therefore (v_(e_1))/(v_(e_2)) = sqrt((R_1 g_1)/(R_2g_2)) = sqrt(Kg) = (Kg)^(1//2)`