Physics Elasticity Question 29
Question: Two rods of different materials having coefficients of linear expansion $ {{\alpha } _{1}},,{{\alpha } _{2}} $ and Young’s moduli $ Y _{1} $ and $ Y _{2} $ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $ {{\alpha } _{1}}:{{\alpha } _{2}}=2:3 $ , the thermal stresses developed in the two rods are equally provided $ Y _{1}:Y _{2} $ is equal to
[IIT 1989]
Options:
A) 2 : 3
B) 1 : 1
C) 3 : 2
D) 4 : 9
Show Answer
Answer:
Correct Answer: C
Solution:
Thermal stress = $ Y\alpha \Delta \theta $ . If thermal stress and rise in temperature are equal then $ Y\propto \frac{1}{\alpha } $
Therefore $ \frac{Y _{1}}{Y _{2}}=\frac{{{\alpha } _{2}}}{{{\alpha } _{1}}}=\frac{3}{2} $
BETA
