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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: |
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Answer» `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)` |
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