Question

Two identical charged spheres suspended from a common point by two mass-less strings of length `l` are initially at a distance d ( `d ltlt l`) apart because of their mutual repulsion . The charge begins to leak from both the spheres at a constant rate. As a result the charge approach each other with a velocity `v`. Then as a function of distance `x` between them .
A. `v prop x^(-1)`
B. `v prop x^((1)/(2))`
C. `v prop x`
D. `v prop x^(-(1)/(2))`

Answer 1

Correct Answer - D

`T sin theta = (kq^(2))/(x^(2))`
`T cos theta = mg`
Dividing the equations
`tan theta = (kq^(2))/(mgx^(2))` here `tan theta ~~ theta = (x)/(2l)`
`rArr (x)/(2l) = (kq^(2))/(x^(2))`
`rArr q prop c^(3//2)`
`rArr (dq)/(dt) prop (3)/(2) x^(1//2) ((dx)/(dt)) rArr (dx)/(dt) prop x^(-1//2)`