Question

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 by

• A. $\frac{5}{4}d$
• B. $\frac{4}{5}d$
• C. $d$
• D. $\frac{d}{5}$

Answer 1

Answer: (A)

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