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3-2.Motion in Plane
medium
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
A${t_P} < {t_Q}$
B${t_P} = {t_Q}$
C${t_P} > {t_Q}$
DAll of these
(IIT-1993)
Solution
(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 ${t_P} < {t_Q}$.
Standard 11
Physics
