The two planets have radius `r_(1) and r_(2)`, densities `d_(1) and d_(2)`. The ratio of acceleration due to gravity on them is :

Options

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

Answer

D

Explanation

`g=(GM)/(R^(2))=(G)/(R^(2))*(4)/(3)pi R^(3) d rArr g=(4)/(3) pi Rd G`
`therefore (g_(1))/(g_(2))=(R_(1)d_(1))/(R_(2)d_(2))`
Thus correct choice is (d).