A ball of mass m with a charge +q can rotate in a vertical plane at the end of a string of length l in a uniform electric field whose lines of force are directed vertically upwards. The horizontal velocity that must be imparted to the ball at top position so that tension in string at the bottom position of the ball is 15 times the weight of the ball is

Imagine you have one end of the string in your hand, at the other end is the charged sphere. Now you can slowly start swinging the sphere like a pendulum. If you go faster and faster, at some point the sphere will no longer swing back, but complete the circle. It will rotate in a vertical plane. Now you just have to equate gravitational, electric and centrifugal force to find the answer.