A particle P is sliding doen a friction hemispherical bow it passes the point A `u(t = 0)`At this instant of time the horizontal component of its velocity is a A bead Q of the same mass an 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 respectively times taken by `P` and `Q` to reach the point `theta` then

Options

A. `t_(P)ltt_(Q)`
B. `t_(P)=t_(Q)`
C. `t_(P)gt t_(Q)`
D. `(t_(P))/(t_(Q))=("length of arc ACB")/("length of chord AB")`

Answer

A

Explanation

P particle has `a_(1)=g sin theta` due to which its horizontal component of velocity gt v