Question

A simple U tube contains mercury to the same level in both of its arms. If water is poured to a height of 13.6 cm in one arm, how much will be the rise in mercury level in the other arm?

Given : density of mercury = 13.6 x 10³ kg m^-3 and density of water = 10³ kg m^-3.

Answer 1

Given, ρ_m = 13.6 × 10³ kg m ^-3, ρ_w = 10³ kg m ^-3

Height to which water is poured in one arm, h_w = 13.6 cm

By pouring 13.6 cm of water, the mercury level in the left arm goes down to point A by x cm, while in the right arm, it rises to point C by x cm. Therefore, BC = h_m = 2x cm

By Pascal's law,

Pressure in the water column = pressure in the mercury column

Therefore, P_A = P_B

⇒ h_w ρ_w g = h_m ρ_m g

⇒ 13.6 × 10³ × g = 2𝑥 × 13.6 × 10³ × g

⇒ 1 = 2𝑥

⇒ 𝑥 = `1/2`​ = 0.5 cm

Hence, the rise in mercury level = 0.5 cm