Work Power Energy question bank (Physics)

A bead $P$ sliding on a frictionless semi-circular string $(A C B)$ and it is at point $S$ at $t =0$ and at this instant the horizontal component of its velocity is $v$. Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $t=0$ along the horizontal string $A B$, with the speed $v$, friction between the beads and the respective strings may be neglected in both cases. Let $t_{P}$ and $t_{Q}$ be the respective times taken by beads $P$ and $Q$ to reach the point $B$, then the relation between $t_{P}$ and $t_{Q}$ is

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