Problem $4$: Capillary action When a very thin tube $($a capillary$)$ is placed in a container of oil, the combined effects of cohesion and adhesion cause the oil to rise up$.$ These competing surface tensions also result in the meniscus $($shape of the surface$)$ to be curved, with a characteristic radius of curvature $.$ Oil has a density of $700$ kg$/$m$3$ and surface tension of $40$ mN$/$m$.$ The cross$-$sectional radius of the capillary tube is $0\mathrm{.}73$ mm and the contact angle of the oil surface at the meniscus with the glass walls is $50.$ A$.$ What is the radius of curvature of the meniscus? B$.$ What is the gauge pressure at the top of the column? Hint: Use the Laplace equation. C$.$ How high does the oil rise in the capillary tube?