An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of 15°C.Both rods have the same diameter.The rods are joined end-to-end to form a rod 60.0 cm long.The coefficients of linear expansion of aluminum and steel are 2.4 x 10^-5 K-1,and 1.2 × 10-⁵K-1,respectively.The temperature is raised to 90°C.The increase in the length of the joined rod,in mm,is closest to:

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The increase in length of the aluminum rod is:$$\Delta L_{Al} = \alpha_{Al} L_{Al} \Delta T = (2.4 	imes 10^{-5} K^{-1})(0.100 m)(90°C - 15°C) = 1.68 	imes 10^{-3} m$$The increase in length of the steel rod is:$$\Delta L_{steel} = \alpha_{steel} L_{steel} \Delta T = (1.2 	imes 10^{-5} K^{-1})(0.800 m)(90°C - 15°C) = 8.64 	imes 10^{-3} m$$The increase in length of the joined rod is:$$\Delta L_{joined} = \Delta L_{Al} + \Delta L_{steel} = 1.68 	imes 10^{-3} m + 8.64 	imes 10^{-3} m = 1.032 	imes 10^{-2} m = 10.32 mm$$The closest answer choice is A) 0.90 mm.

An Aluminum Rod Is 10