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A proton, a deuteron and an α-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field lf rp,rd and rα denote respectively the radii o[ the trajectories of these particles, then

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a

rα=rp

b

rα>rd>rp

c

rα=rd>rp

d

rp=rd=rα

answer is A.

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Detailed Solution

Given that  Kp=Kd=Kα=K (say) We know that qp=e, qd=e  and  qα=2eand mp=m,md=2m and mα=4mFurther r=mVqB=2mKqBHence rp=2mKeBrd=2(2m)KeB=2rpand rα=2(4m)K(2e)B=rpHence rα=rp
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A proton, a deuteron and an α-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field lf rp,rd and rα denote respectively the radii o[ the trajectories of these particles, then