A stone is attached to one end of a string and is whirled in a vertical circle of radius R . Determine the minimum speed the stone can have at the highest point of the circle.

Step-by-step solution

At the highest point of the vertical circle, the forces acting on the stone are its weight mg and the tension T in the string, both acting downwards towards the center of the circle. The equation for centripetal force is given by T + mg = mv^2 R . For the stone to just complete the circle, the minimum speed at the highest point corresponds to the condition where the tension in the string becomes zero ( T = 0 ). Substituting T = 0 in the equation, we get mg = mv^2 R . Solving for v , we get v^2 = Rg v = Rg . Thus, t