Sir please explain me , how to derive upthrust=v*d*g mathematically..

Asked by Himadri | 26th Sep, 2019, 02:08: PM

Expert Answer:

  • 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 | 26th Sep, 2019, 06:42: PM