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 A 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

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$t_{P} = t_{Q}$

All of these

$t_{P} < t_{Q}$

$t_{P} > t_{Q}$

answer is A.

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Detailed Solution

For particle P, motion between A and C will be an accelerated one while between C and B a retarded one. But in any case horizontal component of it's velocity will be greater than or equal to v on the other hand in case of particle Q, it is always equal to v. horizontal displacement of both the particles are equal, so $t_{P} < t_{Q}$

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