The radii of two planets are respectively `R_(1)andR_(2)` and their densities are respectively `rho_(1)andrho_(2)`. The ratio of the accelerations due to gravity `(g_(1)//g_(2))` at their surfaces 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))`
D. `(R_(1)R_(2))/(rho_(1)rho_(2))`

Answer

B

Explanation

`g=(GM)/(R^2)=(G)/(R^2)(4)/(3)piR^(3)rho`
`therefore(g_1)/(g_2)=(R_(1)rho_(1))/(R_(2)rho_(2))`