Problem $4.$ Gate $\backslash ($ A B $\backslash )$ is a quarter circle with $10$ meters wide into the paper and hinged at $\backslash ($ B $\backslash ).$ Find the force needed to keep the gate from opening. The gate is uniform and has a mass $100$ kg $.$ Please show all steps

Hint: Consider the weight of a square with $8-$m side that comprises of the water below and above the gate $($dashed square$).$ Then consider the weight of the water below the gate and think about the difference in the weights and how you can use that to find the vertical force component.