1. A vertical plate consists of rectangular and semicircular portion and has dimensions as shown. It is submerged in a liquid such that the upper edge coincides with the free surface of the liquid. What is the ratio of L/R such that force on the rectangular portion is the same as that on the circular portion? 2. Relevant equations F=γhA 3. The attempt at a solution For rectangular part, since height of it is L and width of it is 2R A=2R*L h=L/2 so force on retangular part is Fr=γ*2RL*L/2=γRL2 for semi circular portion h=L+4R/3∏ A=∏R2/2 ∴Fsc=γ(L+4R/3∏)*∏R2/2 Since Fr=Fsc 2RL2=(L+4R/3∏)∏R2(γ cancelled out) . . L2=∏RL/2+2/3R2 now I'm stuck here. Am I doing this right? or did I misunderstand the problem? English isn't my first language, so bear me.