Good Question of Lorentz Law

A magnetic field exists along the positive $x$ -axis. A neutral particle of mass $3m$ placed at origin explodes in two charged particles of mass $m$ and $2m$ . Particle $m$ moves in a circle with centre $(0,5,0)$ with angular velocity $\omega$ along the negative $x$ -axis. If particles $m$ and $2m$ recombine at $(x,y,z)$ then find $x^2+2y+\dfrac{2z}{\sqrt{3}}$ .

Note: Neglect electromagnetic interactions between particles $m$ and $2m$ after the explosion.