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  4. Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :

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Q. Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :

JEE MainJEE Main 2020Electrostatic Potential and Capacitance

Solution:

$ q \Delta V =\frac{1}{2} m V ^{2}$
$\Rightarrow v =\sqrt{\frac{2 q \Delta V }{ m }} $
$ \therefore \frac{ V _{1}}{ V _{2}}=\sqrt{\frac{ e }{ m } \frac{4 m }{ e }}=2$