A liquid kept in a cylindrical vessel is rotated about vertical axis through the centre of circular base. The difference in the heights of the liquid at the centre of vessel and its edge is ( R = radius of vessel, = angular velocity of rotation, g = acceleration due to gravity)

Step-by-step solution

When the cylindrical vessel is rotated at angular speed about its axis, the velocity of the liquid at the sides is maximum, given by v _ s = r Applying Bernoulli's theorem at the sides and at the center of the vessel, we have P + 1 2 v ²= constant P _ s + 1 2 v _ s ²= P _ c + 1 2 v _ c ² where P _ s = pressure at the sides v _ s = velocity of the liquid at the sides P _ c = pressure at the center v _ c = velocity of the liquid at the center P _ c - P _ s = 1 2 v _ s ²= 1 2 r ² ² ( I ) v _ c =0 Since P _ c is greate