Question

The area of cross-section of the wider tube shown in the figure is $800{\text{cm}}^2$. If a mass of $12\text{kg}$ is placed on the massless piston, the difference in heights $h$ in the level of water in the two tubes will be

• A. $10\text{cm}$
• B. $12\text{cm}$
• C. $15\text{cm}$
• D. $17\text{cm}$

Answer 1

The correct option is C $15\text{cm}$

The pressure on the piston on wider tube side will be due to atmospheric pressure $\left(P_o\right)$ and weight of block.
Pressure on piston,
$P_1=\frac{mg}{A}+P_o$
Similarly, on the other side, pressure at the same level of the thinner tube side,
$P_2=\rho gh+P_o$


According to Pascal's law,

$P_1=P_2$

$\frac{mg}{A}+P_o=\rho gh+P_o$

$\Rightarrow \frac{12\times 10}{800\times {10}^{-4}}=1000\times 10\times h$

$\Rightarrow h=0.15\text{m}=15\text{cm}$

Application: We can observe that a $12\text{kg}$ block can be balanced by just a $15\text{cm}$ difference of liquid level. This feature is used in designing "hydraulic lift".