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`
B. `sqrt(r_1/r_2`
C. `[r_2/r_1]^2`
D. `[r_1/r_2]^2`

Answer

A

Explanation

According to question, force acting on the particle inside magnetic field is given by `F_B =qvBsintheta`
[where e = angle between v and B]
This force Fg provides necessary centripetal force for circular motion of the charged particle.
so, `mv^2/r=qvBsintheta`
Now, for particles x and y and for `theta = 90^cric`
`(M_xV_x)/r_1=qv_xB`
`(m _xV_x^2)/r_2=qv_yB`
From Eqs. (i) and (ii), we get
`(m_xV_x)/(m_yV_y)=r_1/r_2`
As, `V_x/V_y=1`
So, `m_x/m_y=r_1/r_2`