Solution:
d=density of cylinderA=area of cross-section of cylinder using law of floatation,
Using law of floatation,
Weight of cylinder = Upthrust by two liquids
L×A×d×g=nρ×(pL×A)g+ρ(L-pL)Agd=npρ+ρ(1-p)=(np+1-p)ρd={1+(n-1)p}ρ
Two non-mixing liquids of densities ρ and nρ (n>1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d
is put in this container. The cylinder floats with its axis vertical and length pL ( 𝑝<1 ) in the denser liquid. The density d is equal to
d=density of cylinderA=area of cross-section of cylinder using law of floatation,
Using law of floatation,
Weight of cylinder = Upthrust by two liquids
L×A×d×g=nρ×(pL×A)g+ρ(L-pL)Agd=npρ+ρ(1-p)=(np+1-p)ρd={1+(n-1)p}ρ