Moving Charge in a Magnetic Field question from MHT CET 2020 (16 Oct, Shift 2)

Answer: (d)

1. Same path and field means same $r$ and $B$: $K = \dfrac{q^2B^2r^2}{2m} \Rightarrow K \propto \dfrac{q^2}{m}$.
2. Alpha: $\dfrac{(2e)^2}{4m_p} = \dfrac{e^2}{m_p}$; proton: $\dfrac{e^2}{m_p}$. The ratio is 1.
3. $K_p = K_\alpha = 10$ eV
4. So the answer is (d) 10 eV.