Two charged particles each having charge ' q ' and mass ' m ' are… | MHT CET 2024 (3 May, Shift 2)

Q35MHT CET 2024 · 3 MAY · SHIFT 2Medium

Electrostatic Potential Energy

Two charged particles each having charge ' $q$ ' and mass ' $m$ ' are held at rest while their separation is ' $r$ '. The speed of the particles when their separation is ' $\frac{r}{2}$ ' will be ( $\varepsilon_0 =$ permittivity of the medium)

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Answer: (c)

Loss in PE: $\Delta U = \frac{q^2}{4\pi\varepsilon_0}\left(\frac{2}{r} - \frac{1}{r}\right) = \frac{q^2}{4\pi\varepsilon_0 r}$
Both particles move with equal speed: total KE $= 2\cdot\frac{1}{2}mv^2 = mv^2$ .
$mv^2 = \frac{q^2}{4\pi\varepsilon_0 r} \Rightarrow v = \frac{q}{\sqrt{4\pi\varepsilon_0 mr}}$
So the answer is (c).

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Electrostatic Potential Energy question from MHT CET 2024 (3 May, Shift 2)

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