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Question

A cylindrical block of wood floats vertically with 80% of its volume immersed in a liquid at 0C. When the temperature of the liquid is raised to 62.5C, the block just sinks in the liquid. The coefficient of cubical expansion of the liquid is

A
1×103 K1
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B
2×103 K1
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C
3×103 K1
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D
4×103 K1
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Solution

The correct option is D 4×103 K1
Given:
Percentage of volume of cylindrical block immersed in liquid =80%
Initial temperature of liquid, T1=0C
Final temperature of liquid, T2=62.5C
To find:
Coefficient of cubical expansion of liquid, γ=?
We know that,
weight of cylinder = weight of the liquid displaced
Ahρb=0.8×A×h×ρ0


ρ0=ρb0.8=5ρb4 ........(1)
Here, ρ0 is the density of the liquid at 0C and ρb is the density of the block.
Now, due to thermal expansion, density as function of temperature is given by ρ=ρ01+γΔT ......(2)
ρ=5ρb41+γΔT
[from (1) and (2) ]
For the block to sink in the liquid at 62.5C, ρ=ρb
ρb=5ρb41+γΔT
1+γΔT=54
1+γ(T2T1)=54
1+γ(62.50)=54
γ=4×103 C1 or K1

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