Physics

The correct relation for upthrust on a solid of volume V immersed in a liquid of density ρ is :
F_B = $\dfrac{\text{V}_{\text{s}}}{\text{g}}$
F_g = $\dfrac{\text{ρg}}{\text{V}}$
F_B = Vρg
F_g = $\dfrac{\text{V}_{\text{g}}}{\text{ρ}}$

Fluids Upthrust

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Answer

F_B = Vρg

Reason —

Prove that the loss in weight of a body when immersed wholly or partially in a liquid is equal to the buoyant force (or upthrust) and this loss is because of the difference in pressure exerted by liquid on the upper and lower surfaces of the submerged part of the body. Upthrust in Fluids, Archimedes Principle and Floatation, Concise Physics Solutions ICSE Class 9.

Resultant upward thrust on the body

F_B = F₂ – F₂

= h₂ρgA - h₂ρgA

= A(h₂ - h₁)ρg

But, A(h₂ - h₁) = V, the volume of the body submerged in the liquid.

∴ Upthrust F_B = Vρg

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Related Questions

Which of the following are the correct characteristic properties of upthrust ?
(i) the smaller the volume of a body submerged in a liquid, the smaller is the upthrust
(ii) the upthrust acts on the body in an upward direction at the centre of buoyancy
(iii) for the same volume of a body inside a fluid, the less the density of the fluid, greater will be the upthrust
(i) & (ii)
(i) & (iii)
(ii) & (iii)
(i), (ii) & (iii)
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