Properties of Matter 4 Question 15

17. A container of width 2a is filled with a liquid. A thin wire of weight per unit length λ 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(y«a). Determine the surface tension of the liquid.

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(2004, 2M)

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Answer:

Correct Answer: 17. λa2y

Solution:

  1. Free body diagram of the wire is as shown in figure.

Considering the equilibrium of wire in vertical direction, we have

2Tlcosθ=λlg(i)

 For y«a,cosθya

Substituting the values in Eq. (i), we get

T=λa2y



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