Question

A container of width 2a is filled with a liquid. A thin wire of mass per unit length $\lambda$ is gently placed over the liquid surface in the middle of the surface as shown in the figure. As a result, the liquid surface is depressed by a distance $y (\ \textless \ \ \textless \ a)$. Determine the surface tension of the liquid.

Answer 1

The surface tension of the liquid is T = λg/2y

Explanation:

• The free body diagram of wire is shown in figure.
• Let l be the length of wire. If λ is mass per unit length of wire, the weight of wire = (lx) g (acting vertically downward).

Vertical force due to surface tension =2Tl cosθ (upward)

Therefore for vertical equilibrium 2Tlcosθ = (lλ)g

T = λg / 2cosθ

• From the figure

cosθ = y √y^2+a^2 = y/a ( for y << a given)

T = λg / 2(y/a) = λg/2y

Thus the surface tension of the liquid is T = λg/2y

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