Weight of a body on the surfaces of two planets is the same. If their densities are `d_(1) and d_(2)`, then ratio of their radii is

Options

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

Answer

b

Explanation

`W_(1)=W_(2)`
`mg_(1)=mg_(2)`
`(GM_(1))/(R_(1)^(2))=(GM_(2))/(R_(2)^(2))`
`(Gd_(1)(4pi)/(3)R_(1)^(3))/(R_(1)^(2))=(Gd_(2)(4pi)/(3)R_(2)^(3))/(R_(2)^(2))`
`d_(1)R_(1)^(1)=d_(2)R_(2)^(2)`
`(d_(1))/(d_(2))=(R_(2))/(R_(1))`