$2\mathrm{.}5\mathrm{.}13.$ The circular gate shown in Figure $P2\mathrm{.}5\mathrm{.}13$ is hinged at the horizontal diameter. If it is in equilibrium, what is the relationship between $h_A$ and $h_B$ as a function of ${}_A,{}_B,$ and $d?$

Figure P$2\mathrm{.}5\mathrm{.}13$