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. `(R_(1)//R_(2))^(2)`
C. `(R_(2)//R_(1))`
D. `(R_(2)//R_(2))^(2)`

Answer

B

Explanation

`qV=(1)/(2)Mv^(2) or v=sqrt((2qV)/(M))`
`"And "Bqv=(Mv^(2))/(R) or Bq=(Mv)/(R)=(M)/(R)sqrt((2qV)/(M))=(sqrt(2qVM))/(R)" ...(Using (i))"`
`or M=(B^(2)q^(2)R^(2))/(2qV)=(B^(2)qR^(2))/(2V)`
`therefore" "M prop r^(2)" "({:(because "B, q and V are same for the "),("given two particles"):})`
`"Hence "(M_(1))/(M_(2))=((R_(1))/(R_(2)))^(2)`