Two identical charged spheres suspended from a common point by two massless string of length

Question:

Two identical charged spheres suspended from a common point by two massless string of length $\ell$ are initially a distance $\mathrm{d}(\mathrm{d} \ll \ell)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance $x$ between them :- 

  1. $\mathrm{V} \propto \mathrm{X}^{1 / 2}$

  2. $V \propto x$

  3. $\mathrm{V} \propto \mathrm{x}^{-1 / 2}$

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


Correct Option: , 3

Solution:

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