A steel rod of length area of cross-section A, Young's modulus Y and coefficient of linear expansion a is heated through to C. The work done that can be performed by the rod now is :

Question

A steel rod of length area of cross-section A, Young's modulus Y and coefficient of linear expansion a is heated through to C. The work done that can be performed by the rod now is : (A) YA (α t /l)  (B)  12 (YA α t) (l α t) (C)  (1/2) (YA α t) ( (t/2) l α t) (D) 2(YA α t) (l α t )

Tardigrade Admin · Accepted Answer

Work done = (1/2) × Force × Change in length = (1/2) (YA propto t) (l propto t)

Q. A steel rod of length area of cross-section $A$ , Young's modulus $Y$ and coefficient of linear expansion a is heated through $t^{o}$ C. The work done that can be performed by the rod now is :

$Y A \frac{α t}{l}$

$\frac{1}{2} (Y A α t) (l α t)$

$\frac{1}{2} (Y A α t) (\frac{t}{2} l α t)$

$2 (Y A α t) (l α t)$

Work done = $\frac{1}{2} \times F orce \times C han g e in l e n g t h = \frac{1}{2} (Y A \propto t) (l \propto t)$

Q. A steel rod of length area of cross-section A, Young's modulus Y and coefficient of linear expansion a is heated through to C. The work done that can be performed by the rod now is :

YAlαt​

21​(YAαt)(lαt)

21​(YAαt)(2t​lαt)

2(YAαt)(lαt)