Uncategorized: Practice Problem & Solution
A copper rod of $88\text{ cm}$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : (2019) ( $\alpha_{\text{Cu}} = 1.7 \times 10^{-5}\text{ K}^{-1}$ and $\alpha_{\text{Al}} = 2.2 \times 10^{-5}\text{ K}^{-1}$ )
Solution Explained:
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
For the difference in length to be independent of temperature, their expansions must be equal: $L_{\text{Cu}} \alpha_{\text{Cu}} \Delta T = L_{\text{Al}} \alpha_{\text{Al}} \Delta T$. Thus, $88 \times 1.7 \times 10^{-5} = L_{\text{Al}} \times 2.2 \times 10^{-5} \Rightarrow L_{\text{Al}} = 68\text{ cm}$.
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