Question

Two particles X and Y having equal charges, after being acceleration through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii R_1 and R_2, respectively. The ratio of the mass of X to that of Y is

Answer 1

Hence the ratio of the mass of X to that of Y is  m1 / m2 = [ r1 / r2]^2

Explanation:

Radius of circular path traced by a particle r = mv / Bq

Kinetic energy K.E = 1/2 m.v^2 = e.V

  r = √  m^2 v^2 / Bq  

r = √ 2 mK/ Bq

r = √  2meV / Bq

m ∝ r^2

Thus we get the ratio of masses of X to Y  m1 / m2 = [ r1 / r2]^2

Hence the ratio of the mass of X to that of Y is  m1 / m2 = [ r1 / r2]^2

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