Particle sliding down a hemispherical bowl

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. The attempt at a solution

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

N-Mgcosθ = Mv2/R

Mgsinθ = -mvdv/dx

or,Mgsinθ = -mvdv/Rdθ

I am not sure if this is the correct approach.

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

Attached Images
File Type: gif bead.GIF (2.1 KB)

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