A planet is made of two materials of density `p_(1)` and `p_(2)` as shown in figure. Th acceleration due to gravity at surface of planet is same as a depth 'R'. The ratio of `(p_(1))/(p_(2))` is `(a)/(b)`. Find value of `(a^(b)+1)/(86)` (`a` and `b` are lowest possible integers)

Answer

4

Explanation

`(GM)/(2R)^(2)=(GM^('))/(R^(2))`
`(M)/(4)=M`
`(4)/(3)piR^(3)p1+(4)/(3)pi(8R^(3)-R^(3))_(p2)=4((4)/(3)piR^(3)_p1)`
`p_(1)+7p_(2)=4p_(1)`
`(p1)/(p2)=(7)/(3)`