A simple U tube contains mercury to the same level in both of it’s 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

ρ_m = 13.6 x 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

h_w ρ_w g = h_m ρ_m g

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

⇒ 2𝑥 = 1

⇒ x = 1/2 = 0.5 cm

Hence, the rise in mercury level = 0.5 cm