A small bead of mass m is moving on a smooth circular wire (radius R) under the action of a force F directed towards a point P at a distance R/2 from the centre .What should be the minimum velocity of the bead at the point where it is closest to P so that it may complete the circle. I worked it out as follows The bead will complete the circle if it is able to just reach the point diametrically opposite to the nearest point to P because after that a component of F will act along the tangential direction and accelerate the bead. Using conservation of energy 1/2mv^2 + work done by force F >= 0 But i couldn't calculate the work done by the force F. i know W = ∫F.dr so i tried to integrate but i couldnt find the angle between the force and displacement for the integral. Please give some idea on how to work out this integral. Also,can it be done without the integral ?