Heat and Thermodynamics 2 Question 4
7. Two rods, one of aluminium and the other made of steel, having initial length $l _1$ and $l _2$ are connected together to form a single rod of length $l _1+l _2$. The coefficients of linear expansion for aluminium and steel are $\alpha _a$ and $\alpha _s$ respectively. If the length of each rod increases by the same amount when their temperature are raised by $t^{\circ} C$, then find the ratio $\frac{l _1}{l _1+l _2}$
(2003, 2M)
(a) $\frac{\alpha _s}{\alpha _a}$
(b) $\frac{\alpha _a}{\alpha _s}$
(c) $\frac{\alpha _s}{\left(\alpha _a+\alpha _s\right)}$
(d) $\frac{\alpha _a}{\left(\alpha _a+\alpha _s\right)}$
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Answer:
Correct Answer: 7. (c)
Solution:
- Given $\Delta l _1=\Delta l _2$ or $l _1 \alpha _a t=l _2 \alpha _s t$
$$ \therefore \quad \frac{l _1}{l _2}=\frac{\alpha _s}{\alpha _a} \text { or } \frac{l _1}{l _1+l _2}=\frac{\alpha _s}{\alpha _a+\alpha _s} $$
