If a bimetallic strip is heated, it will

$A$ rod of length $20 \, cm$ is made of metal $A$. It expands by $0.075 \, cm$ when its temperature is raised from $0^{\circ}C$ to $100^{\circ}C$. 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 $0.06 \, cm$ for the same change in temperature. The portion made of metal $A$ has the length ............. $cm$.

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:

Write the relation between the coefficient of linear expansion $(\alpha_l)$,coefficient of area expansion $(\alpha_A)$,and coefficient of volume expansion $(\alpha_V)$.

An iron tyre is to be fitted onto a wooden wheel $1 \, m$ in diameter. The diameter of the tyre is $6 \, mm$ smaller than that of the wheel. The tyre should be heated so that its temperature increases by a minimum of ........ $^oC$ (the coefficient of cubical expansion of iron is $3.6 \times 10^{-5} \, ^oC^{-1}$).

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20\,^{\circ}C$,the coefficient of linear expansion (in $^{\circ}C^{-1}$) of the metal is