A charged particle +q of mass m is placed at a distance d from another charged particle -2q of mass 2m in a uniform magnetic field B as shown in the figure. If the particles are projected towards each other with same speed v. After how much time collision will happen. $[v = \frac{qBd}{m}]$

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Radius of + q particle: R = qB m v ​ ; radius of − 2 q particle: R ′ = 2 qB 2 m v ​ = R With v = m qB d ​ : R = d , and both periods T = qB 2 πm ​ are equal Particles collide at the midpoint, each covering 2 d ​ along its circle sin θ = d d /2 ​ = 2 1 ​ ⇒ θ = 6 π ​ = ω t t = 12 T ​ = 12 qB 2 πm ​ = 6 qB πm ​ Answer: (C)

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