Question

The liquids shown in figure in the two arms are mercury (specific gravity $13.6$) and water. If the heights of the mercury column and water column is as shown, find the height $h$ of the water column.

• A. $27\text{cm}$
• B. $12\text{cm}$
• C. $19\text{cm}$
• D. $8\text{cm}$

Answer 1

The correct option is A $27\text{cm}$

Let the atmospheric pressure be $P_o$
Pressure at $A=P_o+h\left(1000\right)g$
Pressure at $B=P_o+\left(0.02\text{m}\right)\left(13600\right)g$
These pressures are equal as $A$ and $B$ are at the same horizontal level. Thus,
$P_o+h\left(1000\right)g=P_o+\left(0.02\text{m}\right)\left(13600\right)g$
$h=0.02\text{m}\times 13.6=0.27\text{m}\Rightarrow h=27\text{cm}$