Two small particles A and B having masses m = 0.5kg each and charge $q_1=(-\frac{155}{18}\mu C)$  and  $q=(+100\mu C)$  respectively, are connected at the ends of a non-conducting, flexible and inextensible string of length r = 0.5m. Particle A is fixed and B is whirled along a vertical circle with centre with centre at A. If a vertically upward electric field of strength $E=1.1\times {10}^{5}N{C}^{-1}$  exists in the space. $(g=10m{s}^{-2})$  choose the correct statement(s)

The minimum velocity of the particle B at the lowest position is $\sqrt{31}$ m/s so that if may just complete the circle.

The minimum velocity of particle B, required at highest point so that if may just complete the circle is $\sqrt{61}m{s}^1$ .

The minimum velocity of particle B, required at highest point so that if may just complete the circle is $\sqrt{67}m/s$ .

The minimum velocity of the particle B at the lowest position is $\sqrt{37}$ m/s so that if may just complete the circle.