NEET 2025 · PhysicsAngle of contactPrevious Year Question
Consider a water tank with one wall at x = L, very wide in the z-direction. When filled with a liquid of surface tension S and density ρ, the liquid surface makes a small angle θ₀ (0 < θ₀ ≪ 1) with the x-axis at x = L. If y(x) is the height of the surface, the equation for y(x) is: (take sinθ(x) ≈ tanθ(x) = dy/dx, g = acceleration due to gravity)
- A.d²y/dx² = ρg/S
- B.dy/dx = ρgx/S
- C.d²y/dx² = ρgx/S
- D.d²y/dx² = ρgy/S✓
Correct Answer
(D) d²y/dx² = ρgy/S
Solution & Explanation
Laplace pressure across the curved surface (small slope) balances the hydrostatic head ρgy: S·(curvature) = ρg·y, and curvature ≈ d²y/dx². Hence d²y/dx² = ρg y / S.
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