Question

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 $pL (p < 1)$ in the denser liquid. The density d is equal to :

• A. $\\{2 + (n + 1) p\\} \rho$
• B. $\\{2 + (n - 1) p\\} \rho$
• C. $\\{1 + (n - 1) p\\} \rho$
• D. $\\{1 + (n + 1) p\\} \rho$

Answer 1

Answer: (C)

$\\{1 + (n - 1) p\\} \rho$

Answer 2

$LAdg = (1 - p) LA \rho g + pLAn \rho g$
$d = (1 - p) \rho + np \rho$
$d = \rho [L - p + np)$
$d = \rho {1 + (n - 1) p}$