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 a speed v. Friction between the bead and the string may be neglected. Let tP and tQ 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. `(t_(p))/(t_(Q)) = ("Length of are" ACB)/("Length of" AB)`

Answer

a

Explanation

As `A` the horizontal speeds of both the masses is the same .The velocity of `Q` remain the same horizontal as so force it acting on the horizontal dipection but it case of P as shown at any internadiate position the horizontal velocity first increase (the as `N sin theta)` reaches a maximum value at O and then decreases this it always remain greater than v Therefore `t_(p) lt t_(Q)`