A particle \[P\] is sliding down a frictionless hemispherical bowl. It passes the point \[A\] at \[t=0\]. At this instant of time, the horizontal component of its velocity is \[v\]. A bead \[Q\] of the same mass as \[P\] is ejected from \[A\] at \[t=0\] along the horizontal string \[AB\] (see figure) with the speed \[v\]. Friction between the bead and the string may be neglected. Let \[{{t}_{P}}\] and \[{{t}_{Q}}\] be the respective time taken by \[P\] and \[Q\] to reach the point \[B\]. Then [IIT 1993]

• A.             \[{{t}_{P}}<{{t}_{Q}}\]
• B.               \[{{t}_{P}}={{t}_{Q}}\]
• C.             \[{{t}_{P}}>{{t}_{Q}}\]
• D.               All of these