Two praticles A and B, having equal charges, after being accelerated through the same potential difference enter a region of uniform magnetic field and the particles descrbe circular paths of radii `R_(1)andR_(2)` respectively. The ratio of the masses of A and B 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)`

Explanation

For a circular path, magnetic force= centripetal force
i.e, `qvB=(mv^(2))/(R)`
Again, `(1)/(2)mv^(2)=qV`
Hence, `qvB=(2qV)/(R)`
or, `R=(2V)/(vB)=(2V)/(B)sqrt((m)/(2qV))" "[":'v=sqrt((2qV)/(m))]`
According to the question, q, V and B are constants.
Therefore, `(R_(1))/(R_(2))=sqrt((m_(1))/(m_(2)))or,(m_(1))/(m_(2))=((R_(1))/(R_(2)))^(2)`