Question

A particle $P$ is sliding down a frictionless hemi-spherical howl. 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 $AB$ with speed $v$. Friction between the bead and the string may be neglected. Let $t_P$ and $t_Q$ be the respective times 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. $\frac{t_P}{t_Q}=\frac{LengthofarcACB}{LengthofAB}$

Answer 1

The correct option is A $t_P<t_Q$

Horizontal displacement of both, the particles and bead, P and Q are equal bead Q moves among AB with a constant velocity v. For particle P, motion between AC will be under acceleration while between CB will be under retardation. The horizontal component of its velocity may be greater than or equal to v. It will not be less than v. So, obviously $t_P<t_Q$.