A uniform solid cylinder of density $0.8$ $g/cm^3$ floats in equilibrium in a combination of two non-mixing liquid $A$ and $B$ with its axis vertical. The densities of liquid $A$ and $B$ are $0.7$ $g/cm^3$ and $1.2$ $gm/cm^3$. The height of liquid $A$ is $h_A = 1.2$ $cm$ and the length of the part of cylinder immersed in liquid $B$ is $h_B = 0.8$ $cm$. Then the length part of the cylinder in air is ....... $cm$
Diffcult
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For equilibrium, Buoyant force $=$ weight of the body
$\Rightarrow h_{A} \rho_{A} A g+h_{B} \rho_{B} A g=\left(h_{A}+h+h_{B}\right) A \rho_{C} g$
(where $\rho_{C}=$ density of cylinder)
$h=\left(\frac{h_{A} \rho_{A}+h_{B} \rho_{B}}{\rho_{C}}\right)-\left(h_{A}+h_{B}\right)=0.25 \mathrm{cm}$
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