Question

A cylindrical vessel is filled with equal amounts of weight of mercury on water. The overall height of the two layers is $29.2\, cm$, 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 $x\, cm$ be the height of mercury in vessel.
The height of water in the vessel $=(29.2 \times x )\, cm$
As per question
$A x \times 13.6 =(29.2-x) \times 1$
or$x =2 \,cm$
$\therefore $ Height of water column $=(29.2-2)=27.2\, cm$
$\therefore $ Pressure of the liquids at the bottom
$=27.2\, cm$ of water column $+2\, cm$ of $Hg$ column
$=\frac{27.2}{13.6}$ of $Hg$ column $+2 \,cm$ of $Hg$ column
$=4\, cm $ of $Hg$ column