A particle of mass 18 gm and charge 1µCis held at rest on a frictionless horizontal surface at a distance of 1m from the fixed charge of 1 milli coulomb. If the particle is released it will be repelled. The speed of the particle when it is at a distance of 10m from the fixed charge is

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100m/s

60m/s

30m/s

45m/s

answer is B.

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Detailed Solution

$\begin{array}{l} KE = ΔU = U_{i} - U_{f} = \frac{q_{1} q_{2}}{4 {πε}_{0}} [\frac{1}{r_{1}} - \frac{1}{r_{2}}] = \frac{1}{2} {mv}^{2} \\ \frac{1}{2} \times (18 \times 10^{- 3}) \times v^{2} \\ = 9 \times 10^{9} \times (1 \times 10^{- 3}) \times 1 \times 10^{- 6} [\frac{1}{1} - \frac{1}{10}] \\ 10^{- 3} v^{2} = \frac{3 \times 3}{10}; v = 30 {ms}^{- 1} \end{array}$

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