Question

A U tube open at both ends contains Hg. 13.6 cm of water is added in left arm. Find the difference in the heights of two levels

• A. 1 cm
• B. 12.6 cm
• C. 1.26 cm
• D. 1.36 cm

Answer 1

Answer: (A)

1 cm

Answer 2

When water (density ρ_w) of height 13.6 cm is added, the extra pressure in the left arm is

$$\Delta P = \rho_{w}\,g\,(13.6\text{ cm}).$$

This extra pressure is balanced by a difference Δh in the mercury (density ρ_Hg = 13.6ρ_w) columns. Thus,

$$\rho_{w}\,g\,(13.6) = \rho_{Hg}\,g\,\Delta h \quad\Longrightarrow\quad \Delta h = \frac{13.6}{13.6} = 1\text{ cm.}$$