A hole is drilled in a copper sheet. The diameter of the hole is 4.24cm at 27∘C. What is the change in the diameter of the hole when the sheet is heated to 227∘C ? [α=1.70×10−5/∘C].
A
1.44×10−2cm
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B
1.96×10−2cm
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C
1.78×10−2cm
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D
1.28×10−2cm
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Solution
The correct option is A1.44×10−2cm Given:
Diameter of the hole, d=4.24cm
Initial temperature, T1=27∘C
Final temperature, T2=227∘C
Co-efficient of linear expansion of copper, α=1.70×10−5/∘C.
To find: Change in diameter, Δd=?
We know that change in linear dimension on heating is given by Δd=αdΔT ⇒Δd=1.70×10−5×4.24×(227−27) ⇒Δd=1.44×10−2cm