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

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{2+(n-1)p}ρ

{1+(n-1)p}ρ

{1+(n+1)p}ρ

{2+(n+1)p}ρ

answer is B.

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Detailed Solution

d=density of cylinder A=area of cross-section of cylinder using law of floatation,Using law of floatation, Weight of cylinder = Upthrust by two liquidsL×A×d×g=nρ×(pL×A)g+ρ(L-pL)Agd=npρ+ρ(1-p)=(np+1-p)ρd={1+(n-1)p}ρ

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