Two identical charged spheres suspended from a common point by two massless strings of length l are initially at a distance d ≪ l apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of distance x between the spheres as:
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Use small-angle approximation and equilibrium conditions for charged pendulums.