Two identical charged spheres suspended from a common point by two massless strings of lengths l , are…

1. $v\propto x^{\frac{1}{2}}$
2. $v\propto x$
3. $v\propto x^{-\frac{1}{2}}$
4. $v\propto x^{-1}$

Solution

$\sin \theta =$ $\theta =\frac{x}{2l}$, $\cos \theta \approx 1$
$f_e\cos \theta =m\mathrm{gsin}\theta$
$f_e=mg.\left(\frac{x}{2l}\right)$
$\frac{k{q}^2}{x^2}=\frac{mgx}{2l}$
$k{q}^2=\frac{mg}{2l}{x}^3$
$q\propto x^{\frac{3}{2}}$
$\frac{dq}{dt}\propto \frac{3}{2} x^{\frac{1}{2}}.\frac{dx}{dt}$
$\Rightarrow x^{\frac{1}{2}}.v=constant$
$v\propto x^{-\frac{1}{2}}$

Asked in: NEET 2016 (Phase 1)

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