Length of the horizontal arm of a uniform cross-section U-tube is l = 5 cm and both ends of the vertical arms are open to the surrounding pressure of 7700 N m - 2 . A liquid of density ρ = 10 3 kg m - 3 is poured into the tube such that the liquid just fills the horizontal part of the tube. Now, one of the open ends is sealed and the tube is then rotated about a vertical axis passing through the other vertical arm wi

Step-by-step solution

Let cross-section area of the tube = A In the right limb for compressed air x = 3 cm p 1 V 1 = p 2 V 2 p 0 A × 6 = p 2 A × 3 p 2 = 2 p 0 . .......(1) ​ Force at the corner of the right limb due to liquid above, F 1 = 2 p 0 + x ρ g A Mass of the liquid in the horizontal arm, m = ρ ( l - x ) A It is rotated about the left limb, then centripetal force, m ω 2 r = ρ l - x A ω 2 × l + x 2 = ρ A ω 2 2 × l 2 - x 2 ρ A ω 2 l 2 - x 2 2 = 2 p 0 + x ρ g A - p 0 A ω = 2 p 0 + x ρ g ρ l 2 - x 2 = 100 rad s - 1