Two non-mixing liquids of densities and are put in a container. The height of each liquid is . A solid cylinder of length and density is put in this container. The cylinder floats with its axis vertical and length in the denser liquid. The density

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Solution

Q.
Two non-mixing liquids of densities $ρ$ and $n ρ$ $(n > 1)$ 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 $p L$ $(p < 1)$ in the denser liquid. The density $d$ is equal to [2016]

1 ${2 + (n - 1) p} ρ$

2 ${1 + (n - 1) p} ρ$

3 ${1 + (n + 1) p} ρ$

4 ${2 + (n + 1) p} ρ$

Ans.
(2)

A = area of cross-section of cylinder

Using law of floatation,

$weight of cylinder = upthrust by two liquids$

$L \times A \times d \times g = n ρ \times (p L \times A) g + ρ (L - p L) A g$

$d = n p ρ + ρ (1 - p) = (n p + 1 - p) ρ$

$d = {1 + (n - 1) p} ρ$

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