The radii of two planets are respectively `R_(1) and R_(2)` and their densities are respectively `rho_(1) and rho_(2)`.The ratio of the accelerations due to gravity at their surface is

Options

A. `(R_1 rho_2)/(R_2 rho_1)`
B. `(R_1 rho_1)/(R_2 rho_2)`
C. `(rho_1 R_2^2)/(rho_2 R_1^2)` s
D. `(R_1 + R_2)/(rho_1 rho_2) `

Answer

B

Explanation

`g = (GM)/(R^2) = (G)/(R^2) 4/3 pi R^3 rho = 4/3 pi GR rho`
` therefore g_1/g_2 = (R_1 rho_1)/(R_2 rho_2)`