A homogenous solid cylinder of length $L (L < H / 2)$ cross-sectional area $\frac{A}{6}$ 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 figure. The lower density liquid is open to atmosphere having pressure $P_{0}$ . Then, density D of solid is given by where A is area of cross section of vessel

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$4 d$

$\frac{4}{5} d$

$\frac{d}{5}$

$\frac{5}{4} d$

answer is A.

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Detailed Solution

For the equilibrium of floating body, Weight of body = Total up thrust

$(\frac{A}{5}) L p g = (\frac{A}{5}) (\frac{3 L}{4}) d g + \frac{A}{5} (\frac{L}{4}) (2 d) g p = \frac{3}{4} d + \frac{d}{2} p = \frac{5 d}{4}$

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