Question

A brass rod of length 500 mm and diameter 3 mm is joined to a steel rod of same length and diameter at $ \text{50}{{\,}^{\text{o}}}\text{C}\text{.} $ If the coefficients of linear expansion of brass and steel are $ 2.5\times {{10}^{-5}}{{\,}^{o}}{{C}^{-1}} $ and $ 1.25\times {{10}^{-5}}{{\,}^{o}}{{C}^{-1}}, $ then change in length of the combined rod at $ 200{{\,}^{o}}C $ is :

• A. 2.4 mm
• B. 2.8 mm
• C. 3.2 mm
• D. 3.6 mm

Answer 1

Answer: (B)

Change in length of brass rod $ \Delta {{l}_{B}}={{\alpha }_{B}}{{l}_{B}}({{T}_{2}}-{{T}_{1}}) $ $ =2.5\times {{10}^{-5}}\times 500\times (200-50) $ $ =1.875\,mm $ Similarly change in length of steel rod $ \Delta {{l}_{S}}={{\alpha }_{S}}{{l}_{S}}({{T}_{2}}-{{T}_{1}}) $ $ =1.25\times {{10}^{-5}}\times 500\times (200-50) $ $ =0.9375\,mm $ Therefore, change in length of the combined rod $ =\Delta {{l}_{B}}+{{l}_{S}}=1.875+0.9375 $ $ =2.8125\,mm=2.8\,mm $