A rectangular gate $($as shown in the figure$)$ of negligible thickness, hinged at its top edge and of width $b,$

separates two tanks in which there is the same liquid of density rho. It is required that the gate shall open

when the level in the left$-$hand tank falls below a distance H from the hinge. The level in the right$-$hand

tank remains constant at a height y above the hinge. Derive an expression for the weight of the gate in

terms of H$,$ Y$,$ y$,$ b and g$.$ Assume that the weight of the gate acts at its centre of area.