Two pith balls carrying equal charges are suspended from a common point by strings of equal length. The equilibrium separation between the balls is r. The strings are now rigidly clamped at half the height. The equilibrium separation becomes: [Diagram: Image]
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Question

Two pith balls carrying equal charges are suspended from a common point by strings of equal length. The equilibrium separation between the balls is r. The strings are now rigidly clamped at half the height. The equilibrium separation becomes: [Diagram: Image]

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G1 Physics · Accepted Answer

Step 1: At equilibrium, kq²/r² = mg tanθ; for small θ, tanθ ≈ (r/2)/y. Step 2: Rearranging, r³ = 2kq²y/(mg), therefore r³ ∝ y. Step 3: When the clamped height is halved, (r′)³ = r³/2. Step 4: r′ = r/∛2.