Let water level be initially at the positions A and B at a height of 60 cm in the U-tube. If the water level is depressed through a distance y in one of limbs from A to A', water rises in the second limb through y from B to B' so that the difference of level in two limbs, A'B', is 2y.
Pressure difference in two limbs = difference in levels × density of water × g = 2y × ρw × g
Restoring force on liquid = 2y × ρw × g × S
where S is area of cross-section of tube.
If m is mass of liquid of height h in each limb initially, m = 2hS × ρw
If a is acceleration imparted to mass m of liquid due to restoring force, a
As acceleration a is directly proportional to vertical displacement and is directed towards the mean positions A or B, the water level executes S.H.M. Its time period T is given by: