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Question
A metal rod is heated to t°C. A metal rod has length, area of cross-section, Young's modulus and coefficient of linear expansion as 'L', 'A', 'Y' and 'a' respectively. When the rod is heated, the work performed is ______.
Options
`1/2"Y AL" alpha^2"t"^2`
`1/2"Y AL"^2 alpha^2"t"^2`
`1/2"Y AL" alpha "t"`
YAL α t
MCQ
Fill in the Blanks
Solution
A metal rod is heated to t°C. A metal rod has length, area of cross-section, Young's modulus and coefficient of linear expansion as 'L', 'A', 'Y' and 'a' respectively. When the rod is heated, the work performed is `underline(1/2"Y AL" alpha^2"t"^2)`.
Explanation:
Work done W = `1/2 "F" l`
where l is the extension
l = L α t
Force F = `("YA"l)/"L"`
`therefore "W" = 1/2 * ("YA"l)/"L"`
`= ("YA"("L"^2 alpha^2"t"^2))/"2L"`
`= 1/2"Y AL" alpha^2"t"^2`
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Thermal Expansion
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