Two particles X and Y having equal charges, after being accelerated 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 masses of X and Y is

Options

A. `sqrt(R_(1)//R_(2))`
B. `R_(1)//R_(2)`
C. `(R_(1)//R_(2))^(2)`
D. `(R_(2)//R_(1))^(2)`

Answer

C

Explanation

Radius of circular orbit of a charged particle in a magnetic field is given by, `r=(mv)/(qB)= (p)/(qB)= (sqrt(2mK))/(qB)`…(i)
Here, K= Kinetic energy of charged particle, charge q is accelerated through some potential difference V. So kinetic energy of charge, K= qV.
From eqn. (i), `r= (sqrt(2mqV))/(qB)`
For given, q, V and B, `r prop sqrtm`
`:. (r_(A))/(r_(B))= sqrt((m_(A))/(m_(B))) or (m_(A))/(m_(B))= ((r_(A))/(r_(B)))^(2)= ((R_(1))/(R_(2)))^(2)`