A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60^° with vertical as shown in…

A small bob $\displaystyle A$ of mass $\displaystyle m$ is attached to a massless rigid rod of length $\displaystyle 1$ m pivoted at point $\displaystyle P$ and kept at an angle of $\displaystyle 60^{\circ}$ with vertical as shown in figure. At distance of $\displaystyle 1$ m below point $\displaystyle P$, an identical bob $\displaystyle B$ is kept at rest on a smooth horizontal surface that extends to a circular track of radius $\displaystyle R$ as shown in figure. If bob $\displaystyle B$ just manages to complete the circular path of radius $\displaystyle R$ upto a point $\displaystyle Q$ after being hit elastically by $\displaystyle \operatorname{bob} A$, then radius $\displaystyle R$ is $\displaystyle \_\_\_\_$ m.