Question

A cylindrical vessel is filled with equal amounts of weight of mercury on water. The overall height of the two layers is $29.2cm$, specific gravity of mercury is $13.6$. Then the pressure of the liquid at the bottom of the vessel is

• A. 29.2 cm of water
• B. 29.2/13.6 cm of mercury
• C. 4 cm of mercury
• D. 15.6 cm of mercury

Answer 1

Answer: (C)

Let, $A$ be the area of cross-section of the cylindrical vessel and $xcm$ be the height of mercury in vessel.
The height of water in the vessel $=(29.2\times x)cm$
As per question
$Ax\times 13.6=(29.2-x)\times 1$
or$x=2cm$
$\therefore$ Height of water column $=(29.2-2)=27.2cm$
$\therefore$ Pressure of the liquids at the bottom
$=27.2cm$ of water column $+2cm$ of $Hg$ column
$=\frac{27.2}{13.6}$ of $Hg$ column $+2cm$ of $Hg$ column
$=4cm$ of $Hg$ column