A proton an an `alpha-`particle, moving with the same velocity, enter a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths descirbed by the proton and `alpha`-particle is

Options

A. `1:2`
B. `1:4`
C. `1:16`
D. `4:1`

Answer

A

Explanation

While describing circular path,the centripetal and centerifugal forces are balancing each other
`implies(mv_^(2))/(r)=qvB`
(as the uniform magnetic field is acting normal to the plane)`implies r=(mv)/(qB)impliesr_(p)/(r_(a))=(m_(P)V)/(eB)xx(2eB)/(m_(a)v)=(2m_(p))/(4m_(p))[as m_(a)=4m_(p)]`
`therefore r_(p) :r_(a)=1:2`