A container of width 2a is filled with a liquid. A thin wire of weight per unit length ` lamda ` 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 ltlt a )`. If the surface tension of the liquid is ` (4 lamda ag )/(ky)`. Then value of k is .

Answer

8

Explanation

Free body diagram of the wire is as shown in the figure.
Considering the equilibrium of wire in vertical direction, we have ` 2 T l cos theta = lamda l g " " …(i) `
For ` Y ltlt a , cos theta ~~ (Y)/(a ) , ` Substituting the values in equation (i), we get ` T = (lamda a )/(2 Y ) therefore k = 8 `