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 `(g_1//g_2)` at their surfaces is

Options

A. `R_(1)d_(1):R_(2)d_(2)`
B. `R_(1)^(2)d_(1):R_(2)^(2)d_(2)`
C. `R_(1)^(3)d_(1):R_(2)^(3)d_(2)`
D. `R_(1)d_(1)^(2):R_(2)^(2)d_(2)^(2)`

Answer

A

Explanation

We know the gravity, `g = (4)/(3)pi GRd`
Here given densities `d_(1) and d_(2)` and radii `R_(1) and R_(2)`
So, `(g_(1))/(g_(2))=((4)/(3)piGR_(1)d_(1))/((4)/(3)piGP_(2)d_(2))rArr(g_(1))/(g_(2))=(R_(1)d_(1))/(R_(2)d_(2))`.