Which method is correct for this problem involving motion of

[Sanchayan Dutta]

My Approach is shown in the picture.

 

[nasu]

It may be that none of the answers are right.
For the first method, are the two electric forces on Q in the same direction, when Q is on top?

 

[Sanchayan Dutta]

It may be that none of the answers are right.
For the first method, are the two electric forces on Q in the same direction, when Q is on top?

yes they are in same direction.

 

[nasu]

Do you think that your diagram represents the situation described in the problem?
I mean "particle B at the highest point".

 

[J Hann]

The tension in the string is zero at the top for the given conditions.
Add the contributions to the tension (centripetal force, weight of the mass, and the two electrical forces
such that the tension is zero.
It might be easier to think of the acceleration at the top (m v^2 / R = weight + the two electrical forces)

 

[haruspex]

yes they are in same direction

They are not. Maybe, as nasu wonders, you are taking Q at the lowest point instead of the highest.
In your method 2, you write that the tension is minimum when Q is at the bottom. What makes you think that?

Add the contributions to the tension (centripetal force, weight of the mass, and the two electrical forces such that the tension is zero

Seems to me that is exactly Sanchayan's method 1, but the execution was lacking.