Topic: Electric charge, conservation, Coulomb's law, superposition· Electrostatics

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…

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 \(v\). Then \(v\) varies as a function of the distance \(x\) between the spheres, as :

1. \(v \propto x^{\frac{1}{2}}\)

2. \(v \propto x\)

3. \(v \propto x^{-\frac{1}{2}}\)

4. \(v \propto x^{-1}\)

Doubtly Asked 30 Oct 2026 NEET UG 2016 Phase 1 Practice test neet Save WhatsApp Report

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Answer: 3. \(v \propto x^{-\frac{1}{2}}\)

Key idea: at equilibrium, the electric force balances the horizontal component of tension.

With \(\tan\theta\approx\dfrac{x}{2l}\): \(\dfrac{kq^2}{x^2}=mg\dfrac{x}{2l}\Rightarrow q^2\propto x^3\), so \(q\propto x^{3/2}\).
Charge leaks at a constant rate: \(\dfrac{dq}{dt}=\)constant \(\propto x^{1/2}\dfrac{dx}{dt}\).
Hence \(v=\dfrac{dx}{dt}\propto x^{-1/2}\).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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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…

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