If two planets of radii `R_(1) and R_(2)` have densities `d_(1) and d_(2)`, then the ratio of their respective acceleration due to gravity is

Options

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

Answer

A

Explanation

We know that `g=(GM_(e ))/(R_(e)^(2)) and d=(M_(e ))/(4/3pi R_(e)^(3))`
`rarr g=(4pi GdR_(e))/(3) rarr g prop R_(e )`
`therefore (g_(1))/(g_(2))=(d_(1)r_(1))/(d_(2)r_(2))`