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_(2))/(R_(1))(rho_(1))/(rho_(2))`
B. `(R_(1))/(R_(2))(rho_(2))/(rho_(1))`
C. `(R_(1)rho_(1))/(R_(2)rho_(2))`
D. `sqrt((R_(1)rho_(2))/(R_(2)rho_(1)))`

Answer

C

Explanation

`g=(GM)/(R^(2))=G(4)/(3)(pi R^(3)rho)/(R^(2))=(4)/(3)pi GR rho`
`therefore (g_(1))/(g_(2))=(R_(1)rho_(1))/(R_(2)rho_(2))`