The length of a steel rod is $5 \ cm$ longer than a copper rod at all temperatures. What are the lengths of the steel and copper rods? (The coefficients of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} C$ and $1.7 \times 10^{-5} /{ }^{\circ} C$,respectively.)

Two rods,one of copper $(Cu)$ and the other of iron $(Fe)$,having initial lengths $L_1$ and $L_2$ respectively,are connected together to form a single rod of length $L_1+L_2$. The coefficients of linear expansion of $Cu$ and $Fe$ are $\alpha_c$ and $\alpha_i$ respectively. If the length of each rod increases by the same amount when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1-L_2}{L_1+L_2}$ will be:

To increase the length of a metal rod by $0.4 \%$,the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $= 20 \times 10^{-6} \ {}^{\circ}C^{-1}$) (in $K$)

$A$ rod of length $10 \, m$ at $0 \, ^oC$ has a linear expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6} \, ^oC^{-1}$,where $x$ is the distance from one end of the rod. The length of the rod at $10 \, ^oC$ is: (in $, m$)

Assertion :- $A$ brass disc is fast fitted in a hole in a steel plate. The system must be cooled to loosen the disc from the hole.
Reason :- The coefficient of linear expansion of brass is greater than the coefficient of linear expansion of steel.

$A$ unit scale is to be prepared whose length does not change with temperature and remains $20\,cm$,using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that the difference between their lengths remains constant. If the length of brass is $40\,cm$,what is the length of iron in $cm$?
($\alpha_{\text{iron}} = 1.2 \times 10^{-5} K^{-1}$ and $\alpha_{\text{brass}} = 1.8 \times 10^{-5} K^{-1}$)