Two planets have the same average density but their radii are `R_(1)` and `R_(2)`. If acceleration due to gravity on these planets be `g_(1)` and `g_(2)` respectively, then

Options

A. `(g_(1))/(g_(2)) = (R_(1)^(3))/(R_(2)^(3))`
B. `(g_(1))/(g_(2))=(R_(2))/(R_(1))`
C. `(g_(1))/(g_(2))=(R_(1)^(2))/(R_(2)^(2))`
D. `(g_(1))/(g_(2))=(R_(1))/(R_(2))`

Answer

D

Explanation

`g=(GM)/(R^(2))=(G)/(R^(2))((4)/(3)pi R^(3)rho)`
`therefore g=(4)/(3)pi RG rho " " therefore g prop R`
(`because (4)/(3)pi G` is constant and both have the same density.)
`therefore (g_(1))/(g_(2))=(R_(1))/(R_(2))`