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NEET2025Physics-Fluid Mechanics

NEET 2025 Physics Surface Tension MCQ Question

Type: MCQ-conceptual-Hard-Class 11

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) = dy/dx, g is the acceleration due to gravity)

Question diagram
A

d²y/dx² = ρg/S x

B

d²y/dx² = ρg/S y

C

d²y/dx² = √(ρg/S)

D

dy/dx = √(ρg/S x)

Correct Answer

Option B

Detailed Explanation

Answer: (B)

Solution:

At any point A on the liquid surface, let the height of liquid be y.

Radius of Curvature (ROC) at point A = ρ

Curvature = 1 / ROC
= (d²y/dx²) / [1 + (dy/dx)²]^(3/2)

Given θ is very small, therefore:

tanθ = dy/dx ≈ 0

Hence,

Curvature = d²y/dx²

Excess pressure due to surface tension:

ΔP = S × Curvature
= S(d²y/dx²)

Hydrostatic pressure at height y:

ΔP = ρgy

Therefore,

ρgy = S(d²y/dx²)

So,

d²y/dx² = (ρg/S) y

Hence, correct option is B .

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