Question

In a given $U-$ shaped tube, open at the left end as that of the right end is closed, if the pressure above the liquid in the right arm is $P$, find the value of $P$. Given $d_1=2\times 13.6{\text{g/cm}}^3$ and $d_2=13.6{\text{g/ cm}}^3.$
[Atmospheric pressure $P_a=76\text{cm}$ of $\text{Hg}$]

• A. $P_a$
• B. $2P_a$
• C. $3P_a$
• D. $4P_a$

Answer 1

The correct option is B $2P_a$

Given,

$d_1=2\times 13.6{\text{g/cm}}^3=27.6\times {10}^3{\text{kg/m}}^3$
$d_2=13.6{\text{g/cm}}^3=13.6\times {10}^3{\text{kg/m}}^3$
$P_a=76\text{cm of Hg}$
$P_a=13.6\times {10}^3\times 0.76\times g$


The line $\text{AB}$ is passing through the same liquid, hence, the pressure in the liquid at the same level is the same, i.e., pressure at point $\text{A}$ and $\text{B}$ are equal.

$\Rightarrow P_A=P_B$ and $P_B=P$

$P_a+d_{1}gy+d_{2}gx=P$

$P_a+(27.2\times {10}^3\times 0.25\times g)+(13.6\times {10}^3\times 0.26\times g)=P$

$P_a+13.6\times {10}^3\times g(0.50+0.26)=P$

$\therefore P=2P_a[\because P_a=13.6\times {10}^3\times g\times 0.76]$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(\text{B}\right)$ is the correct answer.

Why this question ? Key concept : In a same liquid, pressure will be the same at all points at the same level.