Two non-mixing liquids of densities $\rho $ and $n \rho \,(n > 1)$ are put in a container. The height of each liquid is $h.$ A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $\rho L (\rho < 1)$ in the denser liquid. The density $d$ is equal to
NEET 2016, Diffcult
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$d = density\,of\,cylinder$
$A = area\,of\,cross - section\,of\,cylinder$
Using law of floatation,
$Weight\,of\,cylinder = Upthrust\,by\,two\,liquids$
$L \times A \times d \times g = n\rho \times \left( {pL \times A} \right)g + \rho \left( {L - pL} \right)Ag$
$d = np\rho + \rho \left( {1 - p} \right) = \left( {np + 1 - p} \right)\rho $
$d = \left\{ {1 + \left( {n - 1} \right)p} \right\}\rho $
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