The correct option is
A Q√2kmR Given that,
Radius of the ring
=R
Mass of charge
−Q=m
Let the velocity of the charge
−Q is
v when it passes through the centre of the ring.
The potential energy at the centre of the ring,
U=k(Q)(−Q)R=−kQ2R
This is the final potential energy, so,
Uf=−kQ2R
The initial potential energy when charge
−Q is at infinite distance away from the ring is zero. So,
Ui=0.
Now, we know from conservation of Mechanical energy for the system,
Decrease in potential energy
= Increase in kinetic energy
⇒ 0−(−kQ2R)=12mv2−0
⇒12mv2=kQ2R
⇒v=Q√2kmR
Hence, option (b) is correct