question_answer

A proton and an \[\alpha -\]particle (with their masses in the ratio 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform, magnetic field is set up perpendicular to their' velocities, the ratio  of the radii \[{{r}_{p}}:{{r}_{\alpha }}\]of the circular paths described by them will be- [JEE Main 12-Jan-2019 Morning]

A) \[1:3\]

B) \[1:\sqrt{2}\]

C) \[1:2\]

D) \[1:\sqrt{3}\]

Correct Answer: B

Solution :

[b] We know that

Given