Consider a water tank shown in the figure. It has one wall at x = L and can be taken to be very wide in the z direction. When filled with a liquid of surface tension S and density ρ, the liquid surface makes angle θ₀ (θ₀ << 1) with the x-axis at x = L. If y(x) is the height of the surface then the equation for y(x) is:

(take θ(x) = sin θ(x) = tan θ(x) =\(\frac{dy}{dx}, \) g is the acceleration due to gravity)

Question

Question

This question was previously asked in

NEET 2025 Official Paper (Held On: 04 May, 2025)

Answer 1

Correct option is: (2) d²y/dx² = (ρg / S) y

Explanation:

Curvature = 1 / ROC = |d²y/dx²| / (1 + (dy/dx)²)^3/2 ≈ |d²y/dx²| / (1 + 0)^3/2 = d²y/dx²

(dy/dx) ≈ tan θ ≈ 0 (small angle approximation)

Change in pressure, ΔP = S × curvature

ΔP = S × d²y/dx²

Also, ΔP = ρgy

⇒ ρgy = S × d²y/dx²

⇒ d²y/dx² = (ρg / S) y