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