A particle spiraling in a magnetic field

A particle with specific charge \( \alpha:= \frac{q}{m}=10^{8} \textrm{ C/kg} \) enters a bubble chamber where its path can be observed. A magnetic field of induction \( B=10^{-2} \textrm{T}\) is perpendicular to the particle's velocity. The particle experiences a viscous drag force which is approximately proportional to its velocity, that is \[ \vec{F}_{drag}=- k \vec{v}. \] As a consequence of this force, the particle spirals inward. It is observed that after two full rotations the radius of curvature decreases by \(2 \% \). Then the magnetic field is switched off and the particle travels \(L=30 \textrm{cm} \) before coming to a stop. What was the particle's velocity in m/s right before entering the chamber?

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