A $1-m$ diameter cylindrical mass, $M,$ is connected to a $2\mathrm{.}3-m-$wide rectangular gate $($see Figure$).$ The

gate is to open when the water level, $h,$ drops below $3$ m $.$ The following is requested:

a$)$ Determine the hydrostatic force over the gate $(F_R).$

b$)$ Determine the location of the center of pressure $(h_p)$ on the gate.

c$)$ Make the free$-$body diagram of the gate and the resulting equation. Moreover, determine tension

T$.$

d$)$ Make the free$-$body diagram of the cylinder and the resulting equation.

e$)$ Determine the required value for the cylindrical mass $M.$

Neglect friction at the gate hinge and the pulley.

Give your results in SI units.