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VERTICAL CIRCULAR MOTION

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A cylinder of radius R is rotating about its horizontal axis with constant omega=sqrt((5g)/R) . A block of mass m is kept on the inner surface of the cylinder. Block is moving in vertical circular motion without slipping. co–efficient of friction between block and surface of cylinder is mu . If minimum value of mu for complete vertical circular motion of block is (2sqrt(6))/(3x) then find 'x'.

Assertion A ball tied by thread is undergoing circular motion (of radius R) in a vertical plane. (Thread always remains in vertical plane). The difference of maximum and minimum tension in thread is independent of speed (u) of ball at the lowest position (ugtsqrt(5gR)) . Reason For a ball of mass m tied by thread undergoing vertical circular motion (of radius R), difference in maximum and minimum magnitude of centripetal aceleraion of the ball is independent of speed (u) of ball at the lowest position (ugrsqrt5gR)) .