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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

a
rα=rp
b
rα>rd>rp
c
rα=rd>rp
d
rp=rd=rα

detailed solution

Correct option is A

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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