The light cone is in equilibrium under the action of hydrostatic forces of two liquids of densities `rho_(1)` and `rho_(2)`. Find `rho_(1)//rho_(2)`. Find `rho_(1)` and `rho_(2)`.

Answer

`5/16`

Explanation

The upward thrust due to liquid `1=` downward thrust due to liquid `2`.
`F_(1)=F_(2)`

`F_(1)=[rho_(1)piR^(2)(2H)g-rho_(1)(piR^(2)((2H)/3))]g=(4piR^(2)Hrho_(1)g)/3`
`F_(2)=Vrho_(2)g, where `V= volume of the double shaded position
`=piR^(2)H=[(piR^(2)(2H))/3-(pi(R/2)^(2)H)/3]`
`=5/12piR^(2)H=5/12piH^(3)`
Then `(rho_(1))/(rho_(2))=5/16`