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 $\rho_0$ ). Then, the pressure at
KVPY 2017, Diffcult
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(a)
Pressure is same at all the points of base.
i.e. Pressure at $M=$ Pressure at $N$
Also, pressure applied anywhere to the fluid is equally transmitted in all directions.
So, pressure at base $=$ pressure due to oil column of height $h+$ pressure due to water column of height $H$.
$\Rightarrow \rho_o g h+\rho_w g H \Rightarrow g\left(\rho_0 \cdot h+\rho_w H\right)$
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