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 $\theta=135^{\circ}$