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=10\text{ }m $ $ \therefore $ $ \Delta l=10\times 100\times 10\times {{10}^{-6}}={{10}^{-2}}m=1\,cm $ 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.