Question

A vertical $U-$tube of uniform cross-section contains water in both the arms. A $10cm$ glycerin column $(R.D.=1.2)$ is added to one of the limbs. The level difference between the two free surfaces in the two limbs will be

• A. $4cm$
• B. $2cm$
• C. $6cm$
• D. $8cm$

Answer 1

The correct option is B $2cm$

Let the level difference between the two free surfaces in the two limbs is $x$.

The pressure at level AA’ of the water and glycerin are equal and it can be written as,

$P_w=P_h$

${\rho }_{w}g\left(h_h+x\right)={\rho }_{h}g{h}_h$

$x=\frac{{\rho }_h{h}_h-{\rho }_w{h}_h}{{\rho }_w}$

$=\frac{0.1\left(1200-1000\right)}{1000}$

$=0.02m$

Thus, the level difference between the two free surfaces in the two limbs is $2cm$.