An electron of mass `0.90 xx 10^(-30)` kg under the action of a magnetic field moves in a circle of 2.0 cm radius at a speed `3.0 xx 10^6 ms^-1`. If a proton of mass `1.8 xx 10^(-27) kg` was to move in a circle of the same radius in the same magnetic field, then its speed will be

Options

A. `3.0 xx 10^6 ms^-1`
B. `1.5 xx 10^3 ms^-1`
C. `6.0 xx 10^4 ms^-1`
D. cannot be estimated from the given data

Answer

b

Explanation

`Bqv=(mv^2)/r or Bqr=mv`
For electron as well as portion B is the same, r is the same and numerically charge q is same: therefore mv is constant
`m_ev_e=m_pv_p=v_p=((m_e)/(m_p))v_e`
or `v_p=((0.90xx10^-30)/(1.8xx10^-27))(3.0xx10^6)=1.5xx10^3ms^-1`