Two identical charged spheres suspended from a common point

Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (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 the distance x between the spheres, as :

From figure tan θ =	F_c	; θ
	mg

	kq²	=	x
	x² mg		2ℓ

or x³ ∝ q² …(1)
or x^{3/ 2} ∝ q …(2)
Differentiating eq. (1) w.r.t. time

3x²	dx	∝ 2q	dq	but	dq	is constant
	dt		dt		dt

so x²(v) ∝ q Replace q from eq. (2)
x²(v) ∝ x^3/2 or v ∝ x^–1/2