Question

If a bar is made of copper whose coefficient of linear expansion is one and a half times that of iron, the ratio of force developed in the copper bar to the iron bar of identical lengths and cross-sections, when heated through the same temperature range (Young's modulus of copper may betaken to be equal to that of iron) is:

• A. 3/2
• B. 2/3
• C. 9/4
• D. 4/9

Answer 1

Answer: (A)

3/2

Here force developed is given as, $F=Y\alpha tA$
where $YtA$ is constant for both copper and iron rod.
now $F\propto \alpha$
and it is given that coefficient of thermal expansion ${\alpha }_{copper}=\frac{3}{2}{\alpha }_{iron}$
hence $\frac{F_c}{F_i}=\frac{{\alpha }_c}{{\alpha }_i}=\frac{3}{2}$