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 ______.

पर्याय

• `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

Answer 1

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`