ICSE Class 9 Answered

• Let us consider a cylindrical body PQRS of cross-sectional area A. It is immersed in a liquid of density ρ.   

• The upper surface is at a depth of h₁ and the lower surface is at a depth of h₂.
• The pressure on the upper surface is P₁ = h₁ρg. Thus, the downward thrust on the upper surface is  

            F₁=h₁ρgA

• The pressure on the lower surface is P₂ = h₂ρg. Thus, the upward thrust on the lower surface is 

            F₂ = h₂ρgA

• Since h₂ > h₁, we have F₂ > F₁.
• Thus, the resultant upward thrust, i.e. the buoyant force, is 

           F_b = F₂ - F₁ 

           F_b = h₂ρgA - h₁ρgA = (h₂ - h₁) ρgA = Vρg 

Hence proved...