1.

Two identical charged spheres suspended from a common point by two masses strings of length l are initially at a distance d (d lt lt 1) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charge approaches each other with a velocity v. Then as a function of distancex between them

Answer»

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

Solution :The repulsive force between the charged SPHERES,
`F = T sin theta`
Weight of each sphere = `MG = T cos theta`
`:. Tan theta = F/(mg) or x/(2l) = (1/(4PI epsilon_0)(q^2)/(x^2))/(mg) or (x^3)/(2l) = 1/(4 pi epsilon_0) cdot (q^2)/(mg)`
`or q prop^(3//2)`

Difference with respect to t,
`(dq)/(dt) prop 3/2 x^(1/2) (DX)/(dt) or, v prop x^(-1/2) [ :' (dq)/(dt)` = constant].


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