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Question

Two particles X and Y having equal charges after being accelerated thorough the same potential difference enter a region of uniform magnetic field and describe circular paths of radius R1 and R2 respectively. the ratio of mass of X to that of Y is

A
R1/R2
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B
R2/R1
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C
(R1/R2)2
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D
R1/R2
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Solution

The correct option is C (R1/R2)2Given that, The radius of particle X=R1 The radius of particle Y=R2 We know that, Work done of each particle = qV Now, suppose the particle starts from rest, and final kinetic energy is For, X particle, 12m1v21=qV For, Y particle 12m2v22=qV Now, m1v21=m2v22.....(I) Now, from the magnetic force isFm1=qv1B Fm2=qv2B Now, the magnetic force is equal to the centripetal force is For, X m1v21R1=qBv1 m1v1=qBR1 For, Y m2v22R2=qBv2 m2v2=qBR2 Now, putting the value in equation (I) m1(qBR1m1)2=m2(qBR2m2)2 R21m1=R22m2 m1m2=(R1R2)2 Hence, the ratio of the mass is (R1R2)2

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