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Question

A cylindrical body of cross-sectional area A, height H and density ρs is immersed to a depth h in a liquid of density ρ, and tied to the bottom with a string. The tension in the string is



A
ρghA
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B
(ρsρ)ghA
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C
(ρρs)ghA
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D
(ρhρsH)gA
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Solution

The correct option is D (ρhρsH)gA
Let T = Tension in string acting in the downward direction


Weight of body,
W = Mg()
=ρsAHg

Buoyant force,
FB=ρg()
=ρgAh

For equilibrium,
Weight of cylindrical body + Tension in string
= Buoyant force
W + T = FB
or T = FBW
=ρgAhρsAHg
=(ρhρsH)gA

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