    Question

# A piece of metal weighs 46 g in air. When immersed in a liquid of specific gravity 1.24 at 27∘C, it weighs 30 g. When the temperature of liquid is raised to 42∘C, the metal piece weighs 30.5 g. Specific gravity of liquid at 42∘C is 1.20. Calculate the coefficient of linear expansion of metal

A
2.23×105oC1
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B
6.7×105oC1
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C
4.46×105oC1
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D
none of these
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Solution

## The correct option is A 2.23×10−5oC−1Let volume of metal piece be V1 at t∘1C(=27∘C) and V2 at t∘2C(=42∘C). Given weight of metal piece in liquid at 27∘C=30 g. As weight of metal piece in air =46 g, hence loss of weight of metal piece in liquid =46−30=16 g= weight of liquid displaced = volume of liquid × density. ∴16=V1×1.24 or V1=161.24 cm3 Similarlry, V2=46−30.51.20=15.51.20 cm3 Now, V42=V27(1+γΔθ) or V2=V1(1+γΔθ)=V1(1+γ×15) ∴1+15γ=V2V1=15.5/1.2016/1.24=1.0010 ∴γ=6.7×10−5oC−1 ∴α=γ3=2.23×10−5oC−1 Hence, the correct answer is option (a).  Suggest Corrections  0      Similar questions
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