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Question

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

A
rα=rp<rd
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B
rα>rd>rp
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C
rα=rd>rp
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D
rp=rd>rα
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Solution

The correct option is A rα=rp<rd
We know that the radius of circular track in a magnatic field =mvqB.......(i)
Momentum in terms of kinetic field is given by
P=2mK = mv .......(ii)
Using (ii) in (i) we get
r=2mKqB

As all these particles have same kinetic energy and are under same magnetic field so we can say
rmq

By using this we can write
rα:rd:rP=4m2q:2mq:mq
rα:rd:rP=1:2:1

On comparing this we get
rα=rP<rd

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