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Q.

Charge q₂ of mass m revolves around a stationary charge ( $q_{1}$ ) in a circular orbit of radius r. The orbital periodic time of q₂ would be

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a

${[\frac{4 π^{2} m r^{2}}{k q_{1} q_{2}}]}^{1 / 2}$

b

${[\frac{k q_{1} q_{2}}{4 π^{2} m r^{3}}]}^{1 / 2}$

c

${[\frac{4 π^{2} m r^{3}}{k q_{1} q_{2}}]}^{1 / 2}$

d

${[\frac{4 π^{2} m r^{4}}{k q_{1} q_{2}}]}^{1 / 2}$

answer is A.

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Detailed Solution

$\frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r^{2}} = m r ω^{2} = \frac{4 π^{2} m r}{T^{2}}$ $(∵ ω = \frac{2 π}{T})$

$\Rightarrow T^{2} = \frac{(4 π ε_{0}) r^{2} (4 π^{2} m r)}{q_{1} q_{2}}$

$∴ Time period, T = {[\frac{4 π^{2} m r^{3}}{k q_{1} q_{2}}]}^{1 / 2}$

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