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. `g_(1):g_(2)=(rho_(1))/(R_(1)^(2)):(rho_(2))/(R_(2)^(2))`
B. `g_(1):g_(2)=R_(1)R_(2)=rho_(1)rho_(2)`
C. `g_(1):g_(2)=R_(1)rho_(2):R_(2)rho_(1)`
D. `g_(1):g_(2)=R_(1)rho_(1):R_(2)rho_(2)`

Answer

D

Explanation

The value of g at surface
`g=(Gmrho)/(R^(2))=G/(R^(2)) . (4pi)/3 R^(3) rho`
`g=4/3pi GRrho`
So `(g_(1))/(g_(2))=(4/3GR_(1 rho1))/(4/3pi GR_(2rho_(2))`
`implies(g_(1))/(g_(2))=(R_(1rho1))/(R_(2 rho2))`