TS EAMCET · Physics · Thermal Properties of Matter
Two rods of same area of cross-section have lengths \(L\) and \(2 \mathrm{~L}\) and coefficients of linear expansions \(2 \alpha\) and \(\alpha\) respectively. If they are welded to form a composite rod of length \(3 \mathrm{~L}\) then the coefficient of linear expansion of the composite rod is
- A \(\frac{3 \alpha}{2}\)
- B \(3 \alpha\)
- C \(\frac{3 \alpha}{4}\)
- D \(\frac{4 \alpha}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{4 \alpha}{3}\)
Step-by-step Solution
Detailed explanation
Change in length of first rod, \[ \Delta \ell_1=\mathrm{L}(2 \alpha) \Delta \mathrm{T}=2 \mathrm{~L} \alpha \Delta \mathrm{T} \] Change in length of second rod: \[ \Delta \ell_2=(2 \mathrm{~L})(\alpha)(\Delta \mathrm{T})=2 \mathrm{~L} \alpha \Delta \mathrm{T} \text {. } \] Total…
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