Question

A long thin straight uniform wire of negligible radius is supported on the surface of a liquid. The width of the container is `2d` and the wire is kept at its centre, parallel to its length (as shown in figure). The surface of the liquid is depressed by a veritcal distance `y(y lt lt d)` at the centre as shown in figure. If the wire has mass `lambda` per unit length, what is the surface tension of the liquid? igonre end effects.

Answer 1

Balancing upward an downward forces
`2(Tlsintheta) = (lambdal)g`
as angle is very small sin `approx tan theta = (y)/(d)`
`T = (lambdagd)/(2y)`