Question

A liquid of density 800 kg/m$^3$ is used instead of mercury in the Torricelli barometer. What is the height of the liquid column if atmospheric pressure is 76 cm of Hg? (Density of mercury = $13.6 \times 10^3$ kg/m$^3$)

• A. 13.2 m
• B. 12.9 m
• C. 13.6 m
• D. 800 m

Hint:

Use pressure balance: $h_1 \rho_1 = h_2 \rho_2$ when a different liquid replaces mercury in a barometer.

Answer 1

The Correct Option is B

Pressure due to mercury column = $P = h_{\text{Hg}} \cdot \rho_{\text{Hg}} \cdot g$
Given $h_{\text{Hg}} = 0.76$ m, $\rho_{\text{Hg}} = 13.6 \times 10^3$ kg/m$^3$
Same pressure should be balanced by the new liquid column: $h_{\text{liq}} \cdot \rho_{\text{liq}} \cdot g$
So, $h_{\text{liq}} \cdot 800 = 0.76 \cdot 13600$ ⇒ $h_{\text{liq}} = \dfrac{0.76 \cdot 13600}{800} = 12.92$ m
Approximate answer = 12.9 m