Question

Two rods of different materials with coefficients of linear thermal expansion $ {{\alpha }_{1}},{{\alpha }_{2}} $ and Youngs moduli Y1 and Y2 respectively are fixed between two rigid walls. They are heated to have the same increase in temperature. If the rods do not bend and if 0.1 : a: = 2: 3, then the thermal stresses developed in the two rods will be equal when $ {{Y}_{1}}:{{Y}_{2}} $ is equal to

• A. 2:03
• B. 2:05
• C. 3:02
• D. 5:02

Answer 1

The Correct Option is C

Thermal stress $ =Y\times strain $ or $ S=Y\varepsilon $ or $ S=Y\alpha t $ where $ \alpha = $ linear thermal expansion $ Y= $ Youngs modulus Here, $ {{S}_{1}}={{S}_{2}} $ $ \Rightarrow $ $ {{Y}_{1}}\,{{\alpha }_{1}}t={{Y}_{2}}{{\alpha }_{2}}t $ or $ \frac{{{Y}_{1}}}{{{Y}_{2}}}=\frac{{{\alpha }_{2}}}{{{\alpha }_{1}}}=\frac{3}{2} $ Thus, $ {{Y}_{1}}:{{Y}_{1}}=3:2 $