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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 \( A B \) (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
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