A small ball of mass 2x10^-3 kg having a charge of 1 microC is suspended by a string of length 0.8 m. Another identical ball having the same charge is kept at the point of suspension. Determine the minimum horizontal velocity, which shud b imparted to the lower ball so tat it can make complete revolution.

Let u be the speed of the ball at its lowest point and v be its speed at highest point.

At highest point, 3 forces are acting on the ball-

1-Electrostatic repulsion, F=Kq²/L²

2-Weight=mg

3-Tension=T

T=0 if the particle has to just complete the circle and the necessary centripetal force is provided by W-F i.e,

Mv²/L = W - F

On solving, u get v² = 2.4 (m/s)²

Now the electrostatic potential energies at the lowest and highest points are equal. Hence from conservation of energy

Mg(2L) = 1/2 M (u² - v²)

substituting v² = 2.4

we get, u=5.86 m/s

Hope u get it.