Two rods,one of aluminum and the other made of steel,having initial lengths $l_1$ and $l_2$ are connected together to form a single rod of length $l_1 + l_2$. The coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively. If the length of each rod increases by the same amount when their temperature is raised by $t ^\circ C$,then find the ratio $\frac{l_1}{l_1 + l_2}$.
- A$\frac{\alpha_s}{\alpha_a}$
- B$\frac{\alpha_a}{\alpha_s}$
- C$\frac{\alpha_s}{\alpha_a + \alpha_s}$
- D$\frac{\alpha_a}{\alpha_a + \alpha_s}$
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Similar Questions
We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains,say $10 \ cm$. We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that the difference between their lengths remains constant. If $\alpha_{\text{iron}} = 1.2 \times 10^{-5} \ K^{-1}$ and $\alpha_{\text{brass}} = 1.8 \times 10^{-5} \ K^{-1}$,what should be the length of each strip?
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View Solution$A$ bimetallic strip is formed out of two identical strips,one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating,the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius of curvature $R$. Then $R$ is:
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View SolutionWhen the temperature of a metal sphere is increased by $40^{\circ}C$,its volume increases by $0.24\%$. The coefficient of linear expansion of the metal is ....... $^{\circ}C^{-1}$.
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View Solution$A$ $50 \ cm$ iron rod is connected to a $100 \ cm$ aluminum rod at $20^{\circ}C$. If $\alpha_{Fe} = 12 \times 10^{-6} {^{\circ}C}^{-1}$ and $\alpha_{Al} = 24 \times 10^{-6} {^{\circ}C}^{-1}$,what is the effective coefficient of linear expansion of the system?
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