Prob. $2\mathrm{.}10\mathrm{.}11$ p$.$ IP$-26[$Ans: $63566\frac{N}{m}].$

$2\mathrm{.}10\mathrm{.}11$ WP The homogeneous gate shown in Fig. P$2\mathrm{.}10\mathrm{.}11$ consists of one quarter of a circular cylinder and is used to maintain a water depth of $4m.$ That is$,$ when the water depth exceeds $4m,$ the gate opens slightly and lets the water flow under it$.$ Determine the weight of the gate per meter of length.