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

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Physics

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Question

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

A

v µ x^–1/2

B

v µ x^–1

C

v µ x^1/2

D

v µ x

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$sinθ = \frac{{kq}^{2}}{d^{2}}$

cos q = mg

$tanθ = \frac{k}{mg} \cdot \frac{q^{2}}{x^{2}}$

$\frac{x}{2 ℓ} \cdot = \frac{k}{mg} \cdot \frac{q^{2}}{x^{2}}$

$x^{3} = \frac{2 kℓ}{mg} q^{2}$

q² µ x³

q² µ x^3/2

$\frac{dq}{dt} \propto \frac{3}{2} x^{1 / 2} \frac{dx}{dt}$ (dq/dt is constant)

c µ x^1/2 v

v µ x^–1/2

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