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A water bucket of mass m is revolved in a vertical circle with the help of a rope of length r. If the velocity of the bucket at the lowest point is √(7gr ) then the velocity and tension in the rope at the highest point are

Answer :

kvnmurty
The kinetic energy at the lowest point = KE1 = 1/2 m v1² = 1/2 m 7 g r
           = 7/2 * mgr
PE + KE at the highest point of the circle = m g * 2 r + 1/2 m v2²

Using energy conservation,  7/2 mgr = 2mgr + 1/2 m v2²
                        v2 = √(3gr) = speed at the top most point

Tension in the string at the highest point = T
         centripetal force = T + mg
                 m v2² / r = T + mg
                 3mgr = T + mg        =>  T = 2 mg


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