A homogeneous solid cylinder of length L (L < H/2) . Cross sectional area A/5 is immersed s

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9-1.Fluid Mechanics

normal

A homogeneous solid cylinder of length $L (L < H/2)$. Cross sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure $P_0$. Then density $D$ of solid is given by

$\frac {5}{4} d$

$\frac {4}{5} d$

$d$

$\frac {d}{5}$

Solution

Weight of cylinder $=$ upthrust due to both liquids

$\mathrm{V.D.} \mathrm{g}=\left(\frac{\mathrm{A}}{5} \times \frac{3}{4} \mathrm{L}\right) \mathrm{d} \cdot \mathrm{g}+\left(\frac{\mathrm{A}}{5} \times \frac{1}{4}\right) 2 \mathrm{d} \cdot \mathrm{g}$

$\Rightarrow\left(\frac{\mathrm{A}}{5} \times \mathrm{L}\right) \mathrm{Dg}=\frac{\mathrm{A.L.}{d.} \mathrm{g}}{4} \Rightarrow \frac{\mathrm{D}}{5}=\frac{\mathrm{d}}{4}$

$\therefore \quad D=\frac{5}{4} d$

Standard 11

Physics