Work in a rotating frame in which the particles are initially at rest. To catch up with B, particle A has to cover a distance $s=\pi R$. Use $s=ut+\frac12at^2$ where $u=0$ is the initial relative velocity. Solve to find $t$.
When A catches B, it has traced an angle of $\pi$ radians in the rotating frame. If the time to catch up was $T$ then during this time the rotating frame traced out arc length $vT$ which subtends angle $vT/R$ radians.
At the time of collision A's speed is $V=v+aT$ and its angular velocity is $V/R$. Its radial acceleration at this time is $V^2/R$.