TS EAMCET · Physics · Thermal Properties of Matter
Three rods of equal lengths are joined to form an equilateral triangle \(A B C . D\) is the mid-point of \(A B\). The coefficient of linear expansion is \(\alpha_1\) for material of rod \(A B\) and \(\alpha_2\) for material of rods \(A C\) and \(B C\). If the distance \(D C\) remains constant for small changes in temperature, then
- A \(\alpha_1=2 \alpha_2\)
- B \(\alpha_1=4 \alpha_2\)
- C \(\alpha_1=8 \alpha_2\)
- D \(\alpha_1=\alpha_2\)
Answer & Solution
Correct Answer
(B) \(\alpha_1=4 \alpha_2\)
Step-by-step Solution
Detailed explanation
\(C D^2=(A C)^2-(A D)^2=l^2-\left(\frac{l}{2}\right)^2\) After small change in temperature \(C D^2=(A C)^2-(A D)^2\) \(=\left[l\left(1+\alpha_2 t\right)\right]^2-\left[\frac{l}{2}\left(1+\alpha_1 t\right)\right]^2\)…
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