Physics - Circular Motion Question with Solution | TestHub

A particle $\mathrm{P}$ is sliding down a frictionless hemispherical bowl. It passes point $\mathrm{A}$ at $t=0$. At this instant of time, the horizontal component of its velocity is $v$. A bead $\mathrm{Q}$ of the same mass as $\mathrm{P}$ is ejected from $\mathrm{A}$ at $t=0$ along the horizontal string $\mathrm{AB}$, with the speed $v$. Friction between the bead and the string may be neglected. Let $t_{\mathrm{p}}$ and $t_{\mathrm{Q}}$ be the, respective, times taken by $\mathrm{P}$ and $\mathrm{Q}$ to reach the point $\mathrm{B}$. Then