A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis
Initially the whole mass of water was lying on randomly. But, as soon as we start rotating the whole mass of water gets pushed towards the outer planes due to centrifugal force. This increases the amount of water at higher radii. Hence moment of inertia increases.