Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d (d << 7)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $v$. Then as a function of distance x between them,

$v∝x^{-1/2}$

The correct answer is Option 4: $v∝x^{-1/2}$

$tan\theta = \theta = \frac{F}{mg}$

$\frac{kq^2}{mgx^2} = \frac{x}{2l}$

$x^3 \propto q^2$

differentiating with respect to time

$ 3x^2 \frac{dx}{dt}$ = $ 2q\frac{dq}{dt}$

$x^2.v \propto q \text{ where $\frac{dq}{dt}$ is a constant}$

Since $ q\propto x^\frac{3}{2}$

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