Question

When will the velocity of the bead will become zero for the first time?

Answer 1

The positive charge at A will pull the negaitvely charged bead at C towards A.

Similarly the one at B will pull it towards B.

These two forces $F_1$ and $F_2$ respectively, will have their components along CO and perpendicular to CO along the opposite directions.

Magnitude wise both $F_1,F_2$ are equal

The perpendicular components will get cancelled and the components along CO will get added up.

The charge will move towards the centre O and due to inertia, it will continue to move along CO away from O, and it will come to rest at C' due to the resultant opposite force acting on it. Due to this force it will come back to O and continue moving due to inertia.

Thus it will perform Simple Harmonic Oscillation.

The velocity of the bead will become zero for the first time when it reaches C'.