A bucket containing water is revolved in vertical circle of radius r. To prevent the water from falling down, the period of revolution required is ( g = gravitational acceleration)

Step-by-step solution

At the highest point of the vertical circle, the forces acting on the water are its weight mg downwards and the normal reaction N from the bucket downwards. The necessary centripetal force is provided by these forces: mg + N = mv^2 r To prevent the water from falling down, the normal reaction must be greater than or equal to zero ( N 0 ). The minimum speed v is obtained when N = 0 : mg = mv^2 r v = rg The angular velocity corresponding to this minimum speed is: = v r = g r The maximum period of revolution T require