Problem 2.173

A mercury drop shaped as a round tablet of radius \(R\) and thickness \(h\) is located between two horizontal glass plates. Assuming that \(h \ll R,\) find the mass \(m\) of a weight which has to be placed on the upper plate to diminish the distance between the plates \(n\) -times. The contact angle equals \(\theta .\) Calculate \(m\) if \(R=2.0 \mathrm{~cm}, h=0.38 \mathrm{~mm}\) \(n=2.0,\) and \(\theta=135^{\circ}\)