A small sphere of mass m and carrying a charge q is suspende

A small sphere of mass m and carrying a charge q is suspended from one end of a massless, conducting thread. The other end of the thread is attached to the highest point of a ring of radius R. The ring is in the vertical plane and is made of a stiff wire. The ring carries charge Q of the same sign as that of the charge q. Find the length of the thread l such that the sphere, after being deflected from its original lower position, found itself in a new equilibrium position located exactly at the axis of the ring, which is perpendicular to the plane of the ring. Find l if m = 1.0 g, q = 8 × 10-8 C, Q = 9 × 10-8 C, and R = 5.0 cm.

the answer is 6.9 cm but i dont know how to get there

Solution

the length L is calculated as follows:

      mv^2/L = kQq/L^2

     L = kQq/mv^2

        = kQq/m[sqrt[2gR]]^2

        = [9X10^9*9 × 10^-8*8 × 10^-8]/1x10^-3*[sqrt[2*9.8*5*10^-2]^2]

        = 0.066 m

        = 6.6 cm

        = 6.9 cm   (its nearest this value)