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.)

Three rods of equal lengths are joined to form an equilateral triangle $ABC$. $D$ is the mid-point of $AB$. The coefficient of linear expansion is $\alpha_1$ for the material of rod $AB$ and $\alpha_2$ for the material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature, then:

Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \ cm$ longer than the copper rod at any temperature. $[$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$]$

The volume of a metal block increases by $0.225 \%$ when its temperature is increased by $30^{\circ} C$. Hence,the coefficient of linear expansion of the material of the metal block is

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?

If the length of a cylinder on heating increases by $2\%$,the area of its base will increase by ....... $\%$