R and r are the radii of the earth and moon respectively , p_e and P_m are densities of earth and mon respectively . The ratio of the acceleration due to geavity on the surfaces of moon and earth is

Options

A. `R/r. p_e/p_m`
B. `r/R.p_e/p_m`
C. `r/R . P_m/p_e`
D. `R/r. P_m/P_e`

Answer

A

Explanation

Accleration due to gravity is given by ,
g= `(GM)/(R^2)`= `(GVp)/(R^2) = (G(4/3))((piR^3p))/(R^2) = (4)/(3) piGRp`
Therefore `(g_e)/(g_m)=(R_e)/(R_m)xx P_e/rp_m`