# 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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