MHTCET 17 Apr 2026 Shift 2 Paper

Concept:In a cyclotron, the magnetic force acts as the centripetal force and decides how the radius, velocity, and angular velocity of the charged particle are related.Explanation:Consider a charged particle of mass $m$ and charge $q$ moving with speed $v$ in a magnetic field $B$.The magnetic force provides the required centripetal force:$$q v B = \frac{m v^{2}}{r}$$Cancelling one factor of $v$ from both sides, we get:$$q B = \frac{m v}{r}$$Rearranging this expression gives the linear velocity:$$v = \frac{q B r}{m}$$From this relation, as the radius $r$ increases, the linear velocity $V$ also increases.Now, the angular velocity is defined as:$$\omega = \frac{v}{r}$$Substituting the expression for $v$ into this definition:$$\omega = \frac{q B}{m}$$Thus, $\omega$ is independent of the radius and remains constant, provided the particle remains non-relativistic.Therefore, when the radius of the circular path increases, the linear velocity increases while the angular velocity stays the same.Answer:Option B: $V$ increases, $\omega$ remains constant.