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  4. A homogeneous solid cylinder of length L(L>H / 2). Cross-sectional area A / 5 is immersed such that it floats as shown in the figure. The lower density liquid is open to atmosphere having pressure P0. Then density D of solid is given by

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Q. A homogeneous solid cylinder of length $L(L>H / 2)$. Cross-sectional area $A / 5$ is immersed such that it floats as shown in the figure. The lower density liquid is open to atmosphere having pressure $P_{0}$. Then density $D$ of solid is given byPhysics Question Image

Mechanical Properties of Fluids

Solution:

Weight of cylinder = Upthrust due to both liquids
$V \times D \times g=\left(\frac{A}{5} \times \frac{3}{4} L\right) \times d \times g+\left(\frac{A}{5} \times \frac{L}{4}\right) \times 2 d \times g$
$\Rightarrow\left(\frac{A}{5} \times L\right) \times D \times g=\frac{A \times L \times d \times g}{4}$
$\Rightarrow \frac{D}{5}=\frac{d}{4}$
$\therefore D=\frac{5}{4} d$