Question

A homogeneous solid cylinder of length $L(L<H/2)$ and 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 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. $\frac{d}{5}$
• D. None of these

Answer 1

Answer: (A)

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