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

Options

A. `r_1/r_2`
B. `sqrtr_1/r_2`
C. `[r_2/r_1]^(2)`
D. `[r_1/r_2]^(2)`

Answer

D

Explanation

When a particle of mass m and charge q is accelerated under a. P.D. (V), the work done=qV and K.E.`1/2mv^(2).therefore 1/2mv^(2)=qV therefore v=sqrt(2qV)/m` the particle moving with this velocity enters the uniform magnetic field B and `(mv^(2))/r=qvB therefore r=(mv)/(qB)` Using the value of v from (1), we get `r=sqrt(m^(2).(2qV)/m)/(qB)=sqrt(2mqV)/(qB)`. Both particles have the same values of q, V and B `therefore rproptosqrtm and r_1/r_2=sqrt(m_x/M_y)or m_x/m_y=((r_1)/r_2)^(2)`.