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A uniform wire having mass per unit leng...

A uniform wire having mass per unit length `lambda` is placed over a liquid surface. The wire causes the liquid to depress by `y(y lt lt a)` as shown in figure. Find surface tension of liquid. Neglect end effect.

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The free body diagram of wire is shown in figure. Let `l` be the length of wire. If `lamda` is mass per unit lengthh of wire, the weight of wire `=(lx)g`(acting vertically downward).
Vertical force due to surface tension `=2Tlcostheta`(upward)
Therefore for vertical equilibrium `2Tlcostheta=(llamda)g`

`T=(lamdag)/(2costheta)`
From the figure
`costheta=y/(sqrt(y^(2)+a^(2))=y/a` ( for `ylt lta` given)
`T=(lamdag)/(2(y/a))=(lamdag)/(2y)`
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