When `alpha`-particle and proton move perpendicular to uniform magnetic field with same speed then ratio of periodic times of their circular motion will be ______

Options

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

Answer

A

Explanation

For uniform circular motion,
`(mv^(2))/r=Bqv`
`therefore(mv)/r=Bq`
`therefore(m(romega))/r=Bq`
`thereforeomega=(Bq)/m`
`therefore(2pi)/T=(Bq)/m`
`thereforeT=(2pim)/(Bq)(because2piandB" are constants")`
`thereforeTpropm/q`
`thereforeT_(alpha)/T_(p)=m_(alpha)/m_(p)xxq_(p)/q_(alpha)`
`=(4m_(p))/m_(p)xxe/(2e)=2/1=2:1`