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Question

A cylinder of mass m and density ρ hanging from a string is lowered into a vessel of cross-sectional area s containing a liquid of density σ(<ρ) until it is fully immersed. The increase in pressure at the bottom of the vessel is :

A
mρgσs
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B
mgs
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C
mσgρs
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D
Zero
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Solution

The correct option is C mσgρs
ρ = density of cylinder
σ= density of the liquid which is in vessel
Fu = upthrust force
s= cross sectional area of vessel
From Newton's third law,
excess force acting on the liquid is equal force of buoyancy acting on the cylinder.
Hence,
ΔP=Fs=Vσgs=mσgsρ

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