The charge on a particle `Y` is double the charge on particle `X`.These two particles `X` and `Y` 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 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))]^(2)`

Answer

A

Explanation

Accroding to question force acting on the particle inside makgnetic field is given by
`F_(e )=qvB sin theta`[ where `theta` = angle between v and B]
this force `F_(B)` provides necessary centripetal force for circular motion of the charged particle
So `(mv^(2))/(r )=qvB sin theta`
Now for particles x and y and for `theta =90^(@)`
`(m_(x)v_(x)^(2))/(r_(1))=qv_(x)B`
`(my v_(y)^(21))/(r_(2))=qv_(y)B`
from Eqs i and iii we get
`(m_(y)v_(x))/(m_(y)v_(y))=(r_(1))/(r_(2))`
as `(v_(x))/(v_(y))=1` so `(m_(x))/(m_(y))=(r_(1))/(r_(2))`