A rod of length 20 cm is made of metal. It expands by 0.075cm when its temperature is raised from 0°C to 100°C. Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature. A third rod of the same length is composed of two parts, one of metal A and the other of metal B. This rod expands by 0.060 cm for the same change in temperature. The portion made of metal A has the length
Text Solution
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$\Delta L = L_0 \alpha \Delta \theta$
Rod A: 0.075 = 20 × × α α A × × 100 ⇒ ⇒ $\alpha_{A} = \frac{75}{2} \times 10^{-6} / ^{\circ} \mathrm{C}$
rod B: 0.045 = 20 × × α α B × × 100 ⇒ ⇒ $\alpha_{B} = \frac{45}{2} \times 10^{-6} / ^{\circ}C$
For composite rod: x cm of A and (20 – x) cm of B we have
0.060 = x α α A × × 100 + (20 – x) α α B × × 100
$= x \left[ \frac{75}{2} \times 10^{-6} \times 100 + (20 - x) \times \frac{45}{2} \times 10^{-6} \times 100 \right]$
On solving we get x = 10 cm.
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