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## Homework Statement

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.Which bead reaches point B earlier?

## Homework Equations

## The Attempt at a Solution

Let θ be the angle which the particle P makes with the vertical .

N-Mgcosθ = Mv

^{2}/R

Mgsinθ = -Mvdv/dx

or,Mgsinθ = -Mvdv/Rdθ

RMgsinθdθ = -Mvdv

∫

_{β}

^{0}RMgsinθdθ = -∫

_{u}

^{w}Mvdv , where β is the initial angle ; u is the initial velocity and w is the velocity at the bottommost point .

But how to relate initial velocity 'u' with the initial horizontal component of velocity 'v' .

I am not sure if this is the correct approach.

I would be grateful if someone could help me with the problem.

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