Question

A body of density `rho` floats with volume `V_(1)` of its total volume `V` immersed in a liquid of density `rho_(1)` and with the remainder of volume `V_(2)` immersed in another liquid of density `rho_(2)` where `rho_(1)gtrho_(2)`. Find the volume immersed in two liquids. (`V_(1)` and `V_(2)`).

Answer 1

For a floating body in two liquids
Weight of the body`=`Buoyant force of liquid I` +` buoyant force of liquid II
`Vrhog=V_(1)rho_(1)g+V_(2)rho_(2)g`
`Vrho=V_(1)rho_(1)+V_(2)rho_(2)`…………i
also `V=V_(1)+V_(2)`………ii
After solving eqn i and ii we get
`V_(1)=V((rho-rho_(2))/(rho_(1)-rho_(2)))` and `V_(2)=V((rho_(1)-rho)/(rho_(1)-rho_(2)))`