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A charge +Q is uniformly distributed over a thin ring of the radius R. the velocity of an electron at the moment when it passes through the centre O of the ring, if the electron was initially far away on the
axis of the ring is (m = mass of electron, $K = \frac{1}{4 {πε}_{0}}$ )

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$\sqrt{(\frac{KQe}{m})}$

$\sqrt{(\frac{Kme}{QR})}$

$\sqrt{(\frac{KQe}{mR})}$

$\sqrt{(\frac{2 KQe}{mR})}$

answer is A.

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Detailed Solution

We have, $K_{i} + U_{i} = K_{f} + U_{f}$

$0 + 0 = \frac{1}{2} {mv}^{2} + (- e) \frac{KQ}{R}$

$∴ Velocity, v = \sqrt{\frac{2 KQe}{mR}}$

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