$(1)$ Gate $HB$ hinged at $H$ is kept closed using a horizontal cable at $B$ as shown. The gate is

rectangular shaped with $1$ m width $($into the page$)$ and mass of $400$ kg $.$ The cable passes

through a frictionless pulley and is connected to the weight M with mass of $1400$ kg and

volume of $0\mathrm{.}5m^3.$ The weight $M$ is partially submerged under water. The density of water

is $1000k\frac{g}{m^3}$ and the acceleration of gravity is $g=9\mathrm{.}81\frac{m}{s^2}.$ The gate is open to the

atmosphere on top. The dimensions are shown on the figure. Calculate $($a$)$ the tension in

the cable $($in N $)$ and $($b$)$ the percentage of volume of the weight that is submerged under

water. $[$Answer: $($a$)11550$ N $,($b$)44\mathrm{.}5\%]$