Solution
= Solution
The <surface tension> has dimensions $[\gamma]=MT^{-2}$, while $[\rho]=ML^{-3}$ and $[g]=LT^{-2}$. Consequently
$$
\left[\frac{\gamma}{\rho gd^n}\right]=\frac{MT^{-2}}{(ML^{-3})(LT^{-2})L^n}=L^{2-n}.
$$
Matching the dimension of height gives $2-n=1$, so \b[$n=1$]. <Dimensional analysis> fixes this exponent but cannot determine a dimensionless prefactor or a contact-angle dependence.