JEE Main 2026 — 23 January, Evening Shift — Question 32

A bead $P$ sliding on a frictionless semi-circular string ( $A C B$ ) and it is at point $S$ at $\mathrm{t}=0$ 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 $\mathrm{t}=0$ 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