A charged particle A(q, m) placed at origin and another charged particle B(–q, m) placed at (d, 0) are projected towards each other with speed $v_0$ as shown. Uniform magnetic field $B_0(-\hat{k})$ exists in the region. Electrostatic interaction between charged particles is ignored, then choose the correct option(s).

Q. A charged particle $+q$ of mass $m$ is placed at a distance $d$ from another charged particle $-2q$ of mass $2m$ in a uniform magnetic field of induction vector $B$ with direction into the plane of paper (as shown in figure). If particles are projected towards each other with equal speeds $V_0$, the maximum value of the projection speed $V_0$, so that the two particles do not collide is :
(Assume only magnetic force of interaction between particles)

Q. A charged particle +q of mass m is placed at a distanced from another charged particle -2q of mass 2m in a uniform magnetic field B as shown
in fig. If the particles are projected towards each other with same speed v,
find the time after which collision occurs between the particles if projection speed equal $2v_m$

Q. A charged particle +q of mass m is placed at a distanced from another charged particle -2q of mass 2m in a uniform magnetic field B as shown in fig. If the particles are projected towards each other with same speed v,
find the maximum value of projection speed $v_m$ so that the two particles do not collide

Q. A charged particle +q of mass m is placed at a distanced from another charged particle -2q of mass 2m in a uniform magnetic field B as shown in fig. If the particles are projected towards each other with same speed v,
Assuming the collision to be perfectly inelastic, find the radius of the particle in subsequent motion. (Neglect the electric force between the charges)

Q. In region $x>0$ , a uniform and constant magnetic field $\overrightarrow{B_1}=2B_0\overrightarrow{k}$ exists. Another uniform and constant magnetic field $\overrightarrow{B_2}=B_0\hat{k}$, exists in region $x<0$. A positively charged particle of mass $m$ and charge $q$ is crossing origin at time $t=0$ with a velocity $\overrightarrow{u}=u_0\hat{i}$. The particle comes back to its initial position after a time $(B_0,u_0$ are positive constants)