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Q.

Two small metal spheres having equal charge and mass are suspended from some point on the ceiling of a damp room with silk threads of equal length. Let center to center distance between sphere be x,  x<

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answer is 3.

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Detailed Solution

At equilibrium, q24πε0x2cosθ=mg sinθFor small θ,  cosθ→1  and  sinθ≈θ=x/2l⇒q24πε0x2=mgx2l⇒q=x3/2.2πε0mgl⇒dqdt=32(x1/2.2πε0mgl).(dxdt)Put v=dxdt∝x-1/2 ⇒dqdt∝322πε0mglHence N=3..
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