Suppose the charge of a proton and an electron differ slightly. One of them is \(-e,\) the other is \((e+\Delta e).\) If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance \(d\) (much greater than atomic size) apart is zero, then \(\Delta e\) is of the order of?
(Given the mass of hydrogen ${\mathrm{}}_{}$\(m_h = 1.67\times 10^{-27}~\text{kg}\)$$)
1. \(10^{-23}~\text{C}\)
2. \(10^{-37}~\text{C}\)
3. \(10^{-47}~\text{C}\)
4. \(10^{-20}~\text{C}\)

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 sphere, as:

1. \(v \propto x \)

2. \(v \propto x^{-1/2}\)

3. \(v \propto x^{-1} \)

4. \(v \propto x^{1/2}\)${\frac{\mathrm{}}{}}^{}$