Q. 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 $v$. A bead $Q$ of the same mass as $P$ is ejected from $A$ to $t = 0$ 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
A) $t_{p} < t_{Q}$
B) $t_{p} = t_{Q}$
C) $t_{p} > t_{Q}$
D) All of these
Explanation
(a) 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 $t_{P} < t_{Q}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.