Two planets have radii `r_(1) and r_(2)` and densities `d_(1) and d_(2)` respectively. Then the ratio of acceleration due to gravity on them will be :

Options

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

Answer

A

Explanation

The relation between density (d) and acceleration due to gravity (g) is
`" "d=(3g)/(4piR_(e)G)`
`therefore" "d_(1)/d_(2)=g_(1)/r_(1) times r_(2)/g_(2)`
`rArr" "g_(1)/g_(2)=(d_(1)r_(1))/(d_(2)r_(2))`