Two particles `X` and `Y` with equal charges, after being accelerated throuhg 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. `sqrt((r_(1))/(r_(2)))`
C. `[(r_(2))/(r_(1))]^(2)`
D. `[(r_(1))/(r_(2))]`

Answer

D

Explanation

`r=(mv)/(qB)" but",v=sqrt((2qV)/(m))`
`:.r=(m)/(qB)sqrt((2qV)/(m))`
`r=(1)/(B)sqrt((2qV)/(m).(m^(2))/(q^(2)))`
`r=(1)/(B)sqrt((2mV)/(q))`
`rpropsqrt(m)`
`:.mpropr^(2)`
`:.(m_(x))/(m_(y))=((r_(1))/(r_(2)))^(2)`.