Two identical charged spheres suspended form a common point by two massless strings of lengths l, are initially at a distance `d(d gt gt l)` apart because of their mutual repulsion. The charges brgin 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

Options

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

Answer

C

Explanation

`tan theta =F/(mg)`
`implies (x//2)/l = F/(mg) ` ( If `theta` is very small)
`implies x = 2l ((Kq^2)/(x^2mg))`
` implies x^2 prop q^2 implies x^(3//2) propq`
Now, `3/2 x^(1//2) (dx)/(dt) implies v prop x^(-1//2)` [as `(dq)/(dt) ` = Constant]