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.

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