A ball of mass M is hanging from a pivot with the help of a massless chord of length 10 m .Find the minimum horizontal velocity that has to be applied to the stationary ball such that the chord is taut at the highest point of rotation . a ) 19.90 m / s 

Let l be the length of the string; T, the tension in the string ; v _{f} , the final velocity of the ball ; v _{0} , the initial velocity of the ball ; M , the mass of the ball and R , the radius of the circle of rotation of the ball . At the highest point of rotation the equation of motion in the radial direction is,
{ ( M v_{f}^{2} ) / R }  M g  T = 0
or { (
M v_{f}^{2} ) / R }  M g = 0 or (
v_{f}^{2} ) = g R M
g sin q = M (  a _{t} ) 