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NEET 2013 · Electric Charge & Coulomb's Law

Electric Charge & Coulomb's Law question from NEET 2013

Q70NEET 2013Medium

Electric Charge & Coulomb's Law

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes

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Answer: (d)

For each ball $\tan\theta = \dfrac{F}{mg}$ and from the geometry $\tan\theta = \dfrac{r/2}{y}$ .
$\dfrac{kq^2}{r^2 mg} = \dfrac{r}{2y} \Rightarrow r^3 = \dfrac{2kq^2y}{mg} \propto y$
Height becomes $y/2$ : $r'^3 = \dfrac{r^3}{2} \Rightarrow r' = \dfrac{r}{\sqrt[3]{2}}$
So the answer is (d).

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