Two identical charged spheres suspended from a common point by two massless strings of lengths l , are initially at a distance d ( d ≪ l ) apart because of their mutual repulsion. The charges begin to

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Two identical charged spheres suspended from a common point by two massless strings of lengths l , are initially at a distance d ( d ≪ 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 υ . Then υ varies as a function of the distance x between the spheres, asNEET 2016 (Phase 1)

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sin θ = θ = x 2 l , cos θ ≈ 1 f e cos ⁡ θ = m gsin​ θ f e = m g . x 2 l k q 2 x 2 = m g x 2 l k q 2 = m g 2 l x 3 q ∝ x 3 2 d q d t ∝ 3 2 x 1 2 . d x d t ⇒ x 1 2 . v =constant v ∝ x - 1 2

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