Question

The ratio of height of a mercury column in a barometer at a place to the height of the liquid column at the same place are 1:4. Find the density of the liquid in g/$c{m}^3$.

• A. 10.5 g/$c{m}^3$
• B. 4.8 g/$c{m}^3$
• C. 3.4 g/$c{m}^3$
• D. 5.6 g/$c{m}^3$

Answer 1

The correct option is C 3.4 g/$c{m}^3$

Let the density of the liquid be ${\rho }_l$ and mercury be ${\rho }_m$.
Let the height of mercury column be h.
Therefore, height of liquid column be 4h
The bottom pressure will be same for both the liquids since the pressure is same at a horizontal level.
${\rho }_{m}gh$ = ${\rho }_l\times g\times (4h$)
${\rho }_l$ = $\frac{{\rho }_m}{4}$
Since, density of mercury is 13.6 g/$c{m}^3$
${\rho }_l$ = $\frac{13.6}{4}$ = 3.4 g/$c{m}^3$