Problem$-3$; A block is $3\mathrm{.}0m$ long and has a square section with a diagonal $L=2\sqrt[\phantom{2}]{EN}m$ supported by two perpendicular walls to retain water on one side and oil on the bottom comer of the other side. If the oil has a density of $800k\frac{g}{m^3}$ and the block has a density of $2200k\frac{g}{m^3},$ calculate the vertical reaction at $N$ and horizontal reaction at $M.$

Problem$-4$; A wooden solid block with an isosceles triangle cross section $($two sides of equal length$)$ has a height $H=\sqrt[\phantom{2}]{EN}m$ and a base $B=\sqrt[\phantom{2}]{EN}m.$ The block has a length $S=3m$ and density of $650k\frac{g}{m^3}.$ If the block floats on water as show in the figure, find the block metacentric height.

Uniform pressure: $P=gh$;$F=PA$

Nonuniform pressure: $F=g{h}_{e}A$;$h_p=h_{}+\frac{I_{CG}}{h_{e}A}$

For a triangle: $A=B\frac{H}{2}$;$I_{CG}=B\frac{H^3}{36}$;$y_{CG}=\frac{H}{3}$

$F_x=F_B=g{h}_{c}A$

$F_V=W=mg=gV$

$F_s=W$

${}_{z}g{V}_D={}_{b}g{V}_T$

$BM=\frac{I_{00}}{V_D}$

$GM=BM-BG$

Problem $4$