Question

A particle A has charge +q and a particle B has a charge +9q with each of them having the same mass m.If both the particles are allowed to all from rest through the same potential difference, then the ratio of their speed is

• A. $1:2$
• B. $1:\sqrt{3}$
• C. $1:2\sqrt{2}$
• D. none of these

Answer 1

The correct option is B $1:\sqrt{3}$

A charge $=+q$

B charge $=+9q$

mass $=m$

same difference $=?$

ratio of their speed $=?$

$V=\sqrt{mgh}$

$V=$

now, the working formula is,

$\frac{K_a}{K_b}=\frac{q\times V}{9q\times V}$

$\frac{-\frac{1}{2}{mV}_a^2}{\frac{1}{2}{mV}_0^2}=\frac{1}{9}$

or, $\frac{V_a}{V_b}=\frac{1}{3}$

It is the ratio between the kinetic energies between the two parties.

$\frac{1}{3}=\frac{V_A^2}{V_b^2}$

or, $\frac{V_A}{V_b}=\frac{1}{\sqrt{3}}$

or, $V_A:V_b=1:\sqrt{3}$