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What should be the length of steel and copper rods at `0^(@)C` that the length of steel rod is 5 cm longer than copper at all termperature? Given `alpha_(Cu) = 1.7 xx 10^(5) .^(@)C^(-1)` and `alpha_(steel) = 1.1 xx 10^(5) .^(@)C^(-1)`. |
Answer» Let l be the length of copper rod at `0^(@)C`. The length steel rod at `0^(@)C = l + 5` If `Delta T ` is the rise in temperature , then as per question. increaes in length of copper rod = increase in length of steel rod `:. L xx 1.7 xx 10^(-5) xx Delta T = (l+5) xx 1.1 xx 10^(-5) xx Delta T` or `1.7 l = 1.1 l + 5.3` OR `0.6 L = 5.5` or ` l = 5.5//0.6 = 9.17 cm` Thus length of copper rod, `l = 9.17 cm` Length of steel rod = `l+5 = 9.17 + 5` ` = 14.17 cm`. |
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