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# ICSE Class 9 Answered

Sir please explain me , how to derive upthrust=v*d*g mathematically..
Asked by Himadri | 26 Sep, 2019, 02:08: PM
• 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

Fb = F2 - F1

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

Hence proved...

Answered by Shiwani Sawant | 26 Sep, 2019, 06:42: PM

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