A body of density ρ and volume V is lifted through height h in a liquid of density σ(

Question

A body of density ρ and volume V is lifted through height h in a liquid of density σ(<ρ). The increase in potential energy of the body is (A) V(ρ-σ) g h (B) V ρ g h (C) V σ g h (D) zero

Tardigrade Admin · Accepted Answer

Weight of body =V ρ g Buoyant force =V σ g Δ U=-Wc=-(W text wt +W text Buoyant force ) Here, Δ U=-[-(V ρ g) h+(V σ g) h] =V(ρ-σ) g h <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c6c8015374bf22e8cc94e9264dbe11ae-.png" />

Q. A body of density $ρ$ and volume $V$ is lifted through height $h$ in a liquid of density $σ (< ρ)$ . The increase in potential energy of the body is

$V (ρ - σ) g h$

$V ρ g h$

$Vσ g h$

zero

Weight of body $= V ρ g$ Buoyant force $= Vσ g$
$Δ U = - W_{c} = - (W_{wt} + W_{Buoyant force})$
Here, $Δ U = - [- (V ρ g) h + (Vσ g) h]$
$= V (ρ - σ) g h$

Q. A body of density ρ and volume V is lifted through height h in a liquid of density σ(<ρ). The increase in potential energy of the body is

V(ρ−σ)gh

Vρgh

Vσgh