First slide

Fluid statics

Question

Two non-mixing liquids of densites 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 [The cylinder is completely submerged in the liquid]

Easy

A

{1+ (n + 1)p}ρ
B

{2+ (n + 1)p}ρ
C

{2 + (n -1)p}ρ
D

{1 + (n - 1)p}ρ

Solution

Where a body is floating in mixture of liquids, then we can write weight of the cylinder = up thrust on culinder due to denser liquid + up thrust on cylinder due to lighter liquid.
Vdg = V₁d₁g + V₂d₂g
Vd = V₁d₁ + V₂d₂ = V₁(nρ) + V₂ρ
$\large d=\frac {V_1}{V}(n\rho)+\frac {V_2}{V} \rho; V=AL$
$\large V_1=ApL;\;V_2=A(1-p)L$
$\large d=\frac {ApL}{AL}(n\rho)+\frac {Al(1-p)\rho}{AL}$
$\large d=pn\rho+[1-p]\rho=\left \{ 1+(n-1)p \right \}\rho$

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