Q 12-04-158JEE MainJEE Main 2022 (27 Jun, Shift 2)Easy
A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If $r_d$ and $r_p$ are the radii of their circular paths respectively, then the ratio $\dfrac{r_d}{r_p}$ will be $\sqrt x : 1$ where $x$ is ______ .
Numerical value type. Enter your answer.
Answer: 2
$$r = \frac{mv}{qB} = \frac{\sqrt{2mK}}{qB}$$
Same charge and kinetic energy, so $r \propto \sqrt m$:
$$\frac{r_d}{r_p} = \sqrt{\frac{2m_p}{m_p}} = \sqrt2 \Rightarrow x = 2$$
Solution by Sreeraj P, M.Sc Physics