If two rods of length L and 2L having coefficient of linear expansion α and 2α respectively are connected so that total length becomes 3L, the average coefficient of linear expansion of the composition rods equals :
Correct answer: C. 5/3 α
- A. 3/2 α
- B. 5/2 α
- C. 5/3 α
- D. None of these
Explanation
To find the average coefficient of linear expansion for the composite rod, we calculate a weighted average based on the lengths of the individual rods. The first rod has a length L and a coefficient of α, while the second rod has a length of 2L and a coefficient of 2α. The total length of the composite rod is 3L.The average coefficient is given by:(L * α + 2L * 2α) / (L + 2L) = (Lα + 4Lα) / 3L = 5α / 3Thus, the correct average coefficient of linear expansion is 5/3 α.Option A (3/2 α) and Option B (5/2 α) both incorrectly calculate the weighted average, while Option D is incorrect because the correct answer is available among the choices.
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