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. `sqrt(R_1)/R_2`
B. `R_2/R_1`
C. `R_1/R_2`
D. `((R_1)/R_2)`

Answer

D

Explanation

When a charged particle is acclerated through a P.D.(v). The K.E. acquired by it is given by `1/2 mv^(2)=qV`. In this case they have the same charge (q) and the same P.D.(V) `therefore` Their K.E. are equal .`therefore 1/2m_1v_1^(2)=1/2m_2v_2^(2) thereforem_1v_2^(2)=m_2v_2^(2)`When they enter the transverse magnetic feild, the ratio of radii of their paths is given by `(R_1)/R_2=(m_1v_1)/(qB) xx (qB)/(m_2v_2)` (they have same q and B)`therefore(R_1^(2))/(r_2^(2))=(m_1^(2)v_1^(2))/(m_2^(2)v_2^(2))=(m_1(m_1v_1^(2)))/(m_2(m_2v_2^(2)))therefore (R_1^(2))/(R_2^(2))=m_1/m_2`.