Question

A bucket full of water is revolved in a vertical circle of 2m. What should be the maximum time period of revolution so that the water does not fall at the point of maximum height ?

Answer 1

let the velocity at the top of the circle be = V  m/s
let Radius R = 2 meter

The centripetal force on water in the bucket should be more than the gravitational pull.  Then water does not fall.

       m V² / R =  m g      =>    V = √(Rg)  = 2√5  m/sec    as g = 10m/sec 
so velocity of the bucket in the vertical circle must be minimum 2√5 m/s

   then the  period of revolution = T <  2πR/ V = 2.8 sec

Answer 2

Answer:

How did T <2pir/v has been applied

I asked it in here because comments are not available there

Explanation: