Question

An iron bar of length 10 m is heated from $0{}^{\circ }C$ to $100{}^{\circ }C$ . If the coefficient of linear thermal expansion of iron is $10\times {10}^{-6}/{}^{\circ }C,$ the increase in the length of bar is

• A. 0.5 cm
• B. 1.0 cm
• C. 1.5 cm
• D. 2:0 cm

Answer 1

Answer: (B)

The change in length $\Delta$ is proportional to L and $\Delta T$ . Stated mathematically $\Delta l=\alpha L\Delta T$ where $\alpha$ is called the coefficient of linear thermal expansion for the material. Given, $\alpha =10\times {10}^{-6}/{}^{\circ }C,\Delta T=100{}^{\circ }C,$ $L=10m$ $\therefore$ $\Delta l=10\times 100\times 10\times {10}^{-6}={10}^{-2}m=1cm$ Note: For an isotropic material, a will be the same in all the same in all the directions, so we can measure a-simply by measuring the change in length of a rod of the material.