A rectangular gate that is $2m$ wide is located in the vertical wall of a tank containing water as shown in the figure below. It is desired to have the gate open automatically when the depth of water above the top of the gate reaches $7\mathrm{.}3m.($a$)$ At what distance, $d,$ should the frictionless horizontal shaft be located? $($b$)$ What is the magnitude of the force on the gate when it is closed?

$($a$)d=m$

$($b$)F_R=$

$m$