a thin wire ring of radius r has a electric charge q.what will be the increment in the force stretching the wire if a charge Q is placed at the centr of the ring.

I am not going to give you a complete and lucarative solution, just go for the hints.
1. Increament in the force means, stifness produced in the ring due to radialy electrostatic force of repulsion. So you have to find Tension in the ring.
2. Tension is a constant force that acts tangentially, thats why consider a small ring element carrying charge’dq’ of length ‘dl’ making angle ‘d@’ at the centre.
3. This small element would experience a force of repulsion due to charge placed at the centre therefore, there would be two component of tension, verticall(acting radially and would be equal to the force of repulsion) and another (horizontal that would cancel each other)
compute the tension...