A homogeneous solid cylinder of length L $(L < H/2)$ . 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 fig. The lower density liquid is open to atmosphere having pressure $P_0$ . Then density D of solid is given by
Text Solution
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Weight of cylinder = up thrust due to both liquids
$V \times D \times g = \left(\frac{A}{5} \times \frac{3}{4} L \right) \times d \times g + \left(\frac{A}{5} \times \frac{L}{4} \right) \times 2 d \times g$
⇒ ⇒ $\left(\frac{A}{5} \times L \right) \times D \times g = \frac{A \times L \times d \times g}{4}$ ⇒ ⇒ $\underline{D} = \underline{d}$ $\frac{5}{4}$ $\therefore D = \frac{5}{4} d$
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