Question

A charged particle q is shot towards another charged particle Q which is fixed with a speed v.it approaches Q upto a closest distance r and then returns.if q was given a speed 2v,the closest distance of approach would be

Answer 1

All the kinetic energy is being completely converted into potential energy of system of two particles.
In the first case:
1/2 mv^2 =kQq/r
In the second case:
1/2 m〖(2v)〗^2 =kQq/r'
Thus,
r’ =r/4