Water stands upto height h behind the dam as shown in the figure. The front view of the dam gate is also shown in the adjoining figure. Density of water is and acceleration due to gravity is g . If atmospheric pressure force is also considered, then the point of application of total force acting on the dam due to water above O is

Step-by-step solution

Force on dam = Pressure of water Area = ( density of water ) (acceleration due to gravity) (height of water 2 (width of dam) (height of water) aligned F & = ( g h 2 ) [(b-h) h] & = g 2 (b h^2-h^3 ) aligned At equilibrium, atmospheric pressure = pressure on dam So, d F d h =0 array rlrl & & h g 2 (b h^2-h^3 ) & =0 & g 2 (2 b h-3 h^2 ) & =0 & 2 b h-3 h^2 & =0 & & 2 b=3 h b & =3 h / 2 & & b-h= 3 h 2 -h & =h / 2 array is the location where the total weight of water acts at a particular point. To find the point of actio