A uniform U-tube of cross-sectional area 5 cm ^2 contains water of density 1000 kg m ⁻³ . Initially, a valve holds the water such that the difference in liquid levels between the two arms is 40 cm . When the valve is opened, the water begins to oscillate. The maximum kinetic energy acquired by the water is (Take g = 10 m s ⁻² )

Step-by-step solution

The maximum kinetic energy of the water is achieved when it passes through its equilibrium position, i.e., when the liquid levels in both arms are equal. By conservation of mechanical energy, the maximum kinetic energy equals the loss in gravitational potential energy (or the work done by gravity) as the levels equalize. Let the initial difference in height be H = 40 cm = 0.4 m . To reach equilibrium, a liquid column of height H/2 must transfer from the higher arm to the lower arm. The volume of this transferred li