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

Answer

A

Explanation

`v prop x^(-1/2)`

`Tsintheta =F` and `Tcostheta=mg`
`therefore tantheta =F/(mg)`
But `tantheta =(d/2)/(sqrt(l^(2)-d^(2)/4))`
`=(kq^(2))/(d^(2)mg)`
`therefore (kq^(2))/(d^(2)mg)`
`therefore d/(2l) =(kq^(2))/(d^(2)mg) [therefore d lt lt l]`
`therefore q^(2) prop d^(3/2)`
`therefore (dq)/(dt) prop d^(1/2v)`
`therefore v prop 1/d^(1/2)`