Question

A homogeneous solid cylinder of length L(L < $\frac{H}{2}$) . Cross-sectional area $\frac{A}{5}$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $\frac{L}{4}$ 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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Weight of cylinder = upthrust due to both liquids

$V\times D\times g=(\frac{A}{5}\times \frac{3}{4}L)\times d\times g+(\frac{A}{5}\times \frac{L}{4})\times 2d\times g\Rightarrow (\frac{A}{5}\times L)\times D\times g=\frac{A\times L\times d\times g}{4}\Rightarrow \frac{D}{5}=\frac{d}{4}\therefore D=\frac{5}{4}d$