Two identical charged spheres suspended from a common point by two massless strings of lengths I, are initially at a distance `d(d ltlt 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 as:

Options

A. `v prop x^(1//2)`
B. `v prop x`
C. `v prop x^(-1//2)`
D. `v prop x^(-1)`

Answer

C

Explanation

`tan theta=F/(Mg)` (since `theta` small)
`theta=F/(Mg)rArr F= Mg theta`
`(KQ^(2))/x^(2)=Mgx/l`
`Q^(2)=(Mg)/(Kl)x^(3)rArr Q=sqrt((Mg)/(Kl))x^(3//2)`
`((dQ)/(dt))=sqrt((Mg)/(kl))(3/2x^(1//2))((dx)/(dt))=` constant
so `(dx)/(dt) prop x^(-1//2)` or `V prop x^(-1//2) rArr v prop x^(-1//2)`