Two non-mixing liquids of densities ρ and nρ (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 pL ( 𝑝

A
${2 + (n - 1) p} ρ$
B
${1 + (n - 1) p} ρ$
C
${1 + (n + 1) p} ρ$
D
${2 + (n + 1) p} ρ$

Solution:

$d = d e n s i t y o f c y l i n d e r A = a r e a o f c r o s s - s e c t i o n o f c y l i n d e r u \sin g l a w o f f l o a t a t i o n,$

Using law of floatation,

Weight of cylinder = Upthrust by two liquids

$\begin{array}{l} L \times A \times d \times g = n ρ \times (p L \times A) g + ρ (L - p L) A g \\ d = n p ρ + ρ (1 - p) = (n p + 1 - p) ρ \\ d = {1 + (n - 1) p} ρ \end{array}$

Solution:

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