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. `(R_1//R_2)^(1//2)`
B. `(R_2//R_1)`
C. `(R_1//R_2)^2`
D. `(R_1//R_2)`

Answer

C

Explanation

`1/2mv^2=qV` or `v=sqrt((2qV)/m)`
Centripetal force, `(mv^2)=qvB`
`Hence, sqrt((2qV)/m)=((qB)/m)R`
or `R=((2qV)/m)^(1//2)xx1/B`
Here, V, q and B are constant. Hence, `mpropR^2`
So, `(m_1)/(m_2)=((R_1)/(R_2))^2`