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  4. A homogeneous solid cylinder of length L ( L < H / 2), cross-sectional area A is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L / 3 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure P0. Then, density D of solid is given by :-

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Q. A homogeneous solid cylinder of length $L ( L < H / 2)$, cross-sectional area $A$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L / 3$ 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 :-Physics Question Image

Mechanical Properties of Solids

Solution:

image
Bouyant force $=\left( F _{ b }\right)_{ d }+\left( F _{ b }\right)_{2 d }= mg$
(d) $ A \frac{2 L}{3} g+(2 d ) \frac{ AL }{3} g = DALg$
$ D =\frac{4 d }{3}$