A cylinder of diameter d is connected to a gate of width W and height L as shown in the figure. The gate is to open when the water level drops below a certain level H, with the cylinder suspended at a height of h from the bottom. Neglecting friction everywhere, derive an expression for calculating the required mass m of the cylinder. Calculate the required mass for L=W=3 meters, H=2 meters and h=d=1 meter assuming water density is 1000 kg/m^3. 
 

1. A cylinder of diameter d is connected to a gate of width W and height L as shown in the figure. The gate is to open when the water level drops below a certain level H, with the cylinder suspended at a height of h from the bottom. Neglecting friction everywhere, derive an expression for calculating the required mass m of the cylinder. Calculate the required mass for: L=W=3m, H=2m and h=d3D1m assuming water density is p=1000kg/m'. [35%] Cylinder d%3D1% L=3m Gate W=3m H Water Hinge