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_(1)/R_(2))^(2)`
D. None of these

Answer

c

Explanation

Let V be the potential difference through which particles are accelerated. Kinetic energy of particles can be written as follows:
`qV = 1/2 mv^(2) rArr mv = sqrt(2qVm)`
Radius of the circle is given by `r = (mv)/(qB) = sqrt(2qVm)/(qB) `
Now we can write the radius for both the particles as follows :
`R_(1) = sqrt(2qVm_(1))/(qB) & R_(2) = sqrt(2qVm_(2))/(qB) `
On dividing , we get the following :
`m_(1)/m_(2) = R_(1)^(2)/R_(2)^(2)`
Hence, option (c ) is correct.