Question

A liquid $X$ of density $4.2{\text{g/cm}}^3$ is poured upto a height of $12\text{cm}$ in the right limb of an U-tube which contains mercury. Another liquid $Y$ is poured in the left arm with height $10\text{cm}$. If upper level of $X$ and $Y$ are same, then find the density of liquid $Y$. (Take density of mercury ${\rho }_{Hg}=13.6{\text{g/cm}}^3$)

• A. $5.76{\text{g/cm}}^3$
• B. $23.2{\text{g/cm}}^3$
• C. $4.64{\text{g/cm}}^3$
• D. $2.32{\text{g/cm}}^3$

Answer 1

The correct option is D $2.32{\text{g/cm}}^3$

Given, density of liquid $X$
${\rho }_X=4.2{\text{g/cm}}^3$
Density of mercury, ${\rho }_{Hg}=13.6{\text{g/cm}}^3$


Pressure on the line $Y{Y}^{\prime }$ should be same for both the limbs. So
${\rho }_{Y}g{H}_Y+{\rho }_{Hg}g\times 2={\rho }_{X}g{H}_X$
$\Rightarrow {\rho }_Y\times 10+13.6\times 2=4.2\times 12\because [H_X=12\text{cm}\&H_Y=10\text{cm}]$
$\therefore$Density of liquid $Y$,
${\rho }_Y=2.32{\text{g/cm}}^3$