Q. A doubly ionized helium ion and a $H_{2}$ ion are accelerated through the same potential. The ratio of the speed of helium and $H_{2}$ ion is
A) 2 : 1
B) 1 : 2
C) 1 : $\sqrt{2}$
D) $\sqrt{2}\ :1$
Explanation
(c) As , $q\ V = \frac{1}{2}\ m\ v^{2}$
Or $v = \ \sqrt{2q\ V/m}$;
So, $v\ \propto \ \sqrt{q\ /m}$ $\therefore\frac{v_{2}}{v_{1}}\ \propto \ \ \sqrt{\frac{2q/4m}{q/m}}$ = $\frac{1}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.