Question

As shown in the figure, pressure acting on the two limbs of a $U-$tube are $P\&P_0$ respectively. Then, identify the correct relation between $P\&P_0$:

• A. $P<P_0$
• B. $P>P_0$
• C. $P=P_0$
• D. $P=P_0=0$

Answer 1

The correct option is A $P<P_0$

Pressure at the same level in the same liquid will be equal.
$\Rightarrow P+{\rho }_{1}g{h}_1=P_0+{\rho }_{2}g{h}_2...\left(i\right)$
Here,
$P=$ atmospheric pressure acting on the left limb of $U-$tube
$P_0=$ atmospheric pressure acting on the right limb of $U-$tube
${\rho }_1=\rho ,h_1=3h,{\rho }_2=2\rho$
$h_2=h$

Substituing in Eq.$\left(i\right)$,
$P+\rho g\left(3h\right)=P_0+\left(2\rho \right)gh$
$\Rightarrow P=P_0-\rho gh$
Hence, we can see that pressure $P$ is lesser than pressure $P_0$
$\therefore P<P_0$