Question

A cylindrical vessel of base radius R and height H has a narrow neck of height h and radius r at one end(see figure). The vessel is filled with water(density ${\rho }_w$) and its neck is filled with immiscible oil (density ${\rho }_o$). Then the pressure at :

• A. M is $g(h{\rho }_o+H{\rho }_w)$
• B. N is $g(h{\rho }_o+H{\rho }_w)\frac{r^2}{R^2}$
• C. M is $gH{\rho }_w$
• D. N is $g\frac{{\rho }_{w}H{R}^2+{\rho }_{o}h{r}^2}{R^2+r^2}$

Answer 1

Answer: (A)

M is $g(h{\rho }_o+H{\rho }_w)$

Pressure at M equals pressure at N (same depth) which is given by:

$P_M=P_N={\rho }_{w}gH+{\rho }_{o}gh$