Question

# A piece of metal weighs 45 g in air and 25 g in a liquid of density 1.5×103kg−m−3 kept at 30C.When the temperature of the liquid is raised to 40C, the metal piece weighs 27 g. The density of liquid at 40C is 1.25×103kg−m−3. The coefficient of linear expansion of metal is

A
1.3×103/C
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B
5.2×103/C
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C
2.6×103/C
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D
0.26×103/C
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Solution

## The correct option is C 2.6×10−3/CThe volume of the metal at 30∘C isV30=lossofweightspecificgravity×g=45×25g1.5×g=13.33cm3Similarly, volume of metal at 40∘CV40=40−27g1.25×g=14.40cm3Now, V40=V301+γt2−t1Or γ=V40−V30V30t2−t1=14.40−13.33113.334.−30=8.03×10−3/∘C∴ Coefficient of linear expansion of the metal isa=γ3=8.03×1033≈2.6×103/∘C

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