Question

A vertical U-tube of uniform cross-section contains water in both the arms. A $12\text{cm}$ glycerine column (Relative density $=1.2$) is added to one of the limbs. The level difference between the two surfaces of both the limbs will be

• A. $2\text{cm}$
• B. $1.2\text{cm}$
• C. $2.4\text{cm}$
• D. $4.8\text{cm}$

Answer 1

The correct option is C $2.4\text{cm}$

Given, height up to which glycerine filled, $\left(h\right)=12\text{cm}$
Let the level difference between 2 limbs be $x$.


Density of glycerine, $\left({\rho }_g\right)=1.2\times 1000=1200{\text{kg/m}}^3$
Density of water $\left({\rho }_w\right)=1000{\text{kg/m}}^3$
Pressure on the line $Y{Y}^{\prime }$ should be same below both limbs, so
$P_o+{\rho }_g\times g\times h=P_o+{\rho }_w\times g(h+x)$
where $P_o$ is atmospheric pressure.
$\Rightarrow 1200\times g\times h=1000\times g(h+x)$
$\Rightarrow 1200\times 0.12=1000(0.12+x)$
$\Rightarrow x=0.024\text{m}=2.4\text{cm}$