Problem $3(20$ points$).$ A rectangular gate is used to release water from a large reservoir water reaches a certain dangerous level. The gate has a length of $5$ m and width $($into the $1$ m and is hinged at its bottom edge as shown in the figure. Under regular operating co the gate is kept closed by a cable, tensioned by hanging a cylindrical block of length $L=$ density ${}_b=8,000k\frac{g}{m^3}.$ What diameter should the block have if the gate is to open water level surpasses $3$ m $?$ Assume that the weight of the gate is negligible, the hinge is fri the block is fully submerged and any drag on the block is negligible. The density of wate $1,000k\frac{g}{m^3}.$

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