Question

The initial lengths of two rods A and B are in the ratio 3:5 and coefficients of linear expansion are in the ratio 5:3. If the rods are heated from ${34}^{\circ }C$ to ${65}^{\circ }C$, the ratio of their expansion will be

• A. 1:1
• B. 3:5
• C. 1:2
• D. 2:3

Answer 1

The correct option is A 1:1

Linear expansion = $L_0\alpha \Delta T$
So ratio = $\frac{L_1{\alpha }_1\Delta T_1}{L_2{\alpha }_2\Delta T_2}$
= $\frac{3\times 5\times 31}{5\times 3\times 31}$
= 1 : 1