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Question

# A body of volume V and density ρ is initially submerged in a liquid of density ρ′. If it lifted through a height h in the liquid, its potential energy will:

A
increase by hV(ρρ)g
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B
decrease by hV(ρρ)g
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C
increase by hVρg/ρ
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D
decrease by hVρg/ρ
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Solution

## The correct option is A increase by hV(ρ−ρ′)gBuoyant force(FB)=ρ′vgFnet=ρvg−FB=ρvg−ρ′g=(ρ−ρ′)vgwork done in lifting the body upto height 'h'ω=→F⋅→s=FScosθ=Fnethcos(180o)ω=−Fnethω=−(ρ−ρ′)vgsince, change in potential energy (ΔU):ΔU=−(Δω)So,ΔU=−ω=−[−(ρ−ρ′)vg]⇒ΔU=(ρ−ρ′)vgSo,Increase in potential energy by (ρ−ρ′)vg.

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