question_answer 10)

A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at \[{{250}^{o}}C\], if the original lengths are at \[{{40}^{o}}C\]? Coefficient of linear expansion of brass and steel are \[10x=7\cdot 35-7x\]\[x=0\cdot 4324m\] and \[=43\cdot \text{2 cm}\]\[1\cdot 0\]respectively.

Answer:

\[0\cdot 5\times {{10}^{-2}}c{{m}^{2}}\]\[g=10m{{s}^{-2}};\]cm. \[Y=2\times {{10}^{11}}N{{m}^{-2}}.\]\[AC=CB=l=0\cdot 5m;\]\[m=100g=0\cdot 100kg\] \[AD=BD={{\left( {{l}^{2}}+{{x}^{2}} \right)}^{1/2}}\] cm. \[\vartriangle l=\text{AD+DB-AB=2AD-AB}\] Change in length of combined rod \[=2{{\left( {{l}^{2}}+{{x}^{2}} \right)}^{1/2}}-2l=2l{{\left( 1+\frac{{{x}^{2}}}{{{l}^{2}}} \right)}^{1/2}}\] cm.