Q 11-10-006NEETJEE MainEAMCET 2014 (Engineering)Medium
What lengths of brass and iron rods at $0°$C must be used if the difference between their lengths is always $0.2$ m? The coefficients of linear expansion of brass and iron are $18 \times 10^{-6}\ °\text{C}^{-1}$ and $12 \times 10^{-6}\ °\text{C}^{-1}$ respectively.
Answer: (A) brass $0.4$ m, iron $0.6$ m
The difference stays constant only if both rods expand by the same amount: $l_b\alpha_b = l_i\alpha_i$, so $\dfrac{l_i}{l_b} = \dfrac{18}{12} = \dfrac{3}{2}$. The iron rod is longer.
With $l_i - l_b = 0.2$ m: $l_b = 0.4$ m and $l_i = 0.6$ m.
Solution by Sreeraj P, M.Sc Physics