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

1. v ∝ x²
2. v ∝ x
3. v ∝ 1/x²
4. v ∝ x⁻¹

Correct answer: v ∝ x⁻¹

Solution

As the charges leak, the electrostatic force decreases, causing the spheres to approach each other. The velocity v is proportional to the rate of change of force, which depends on the inverse square of the distance x. Thus, v ∝ x⁻¹.

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