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, with the 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:

Options

A. `t_(P) lt t_(Q)`
B. `t_(P) = t_(Q)`
C. `t_(P) gt t_(Q)`
D. All of these

Answer

A

Explanation

For particle P, motion between A and C will be an acceleration one white 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) lt t_(Q)`