A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 c m and its rotational speed is 2 rotations per second, then the difference in the heights between the center and the sides, in c m , will be:

Step-by-step solution

When cylinder is rotated, water will rise at the edge and will dip at the centre. The difference in pressure at A and O is P A - P 0 = ρ g h . Due to height difference. pressure difference P 1 - P 0 = ρ ⋅ a c m R Due to rotation. = ρ ⋅ ω 2 . R 2 R ∴ ρ g h = ρ ω 2 R 2 2 ⇒ h = ω 2 ⋅ R 2 2 g = 2 π × 2 2 × 0.05 2 2 × 10 = 0.02 m = 2 c m