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:

What will happen if a rod is tied with fixed supports rigidly at both ends and its temperature is increased?

Suppose there is a hole in a copper plate. On heating the plate,the diameter of the hole will:

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:

$A$ cylinder has a piston at a temperature of $30^{\circ} C$. There is an all-round clearance of $0.08 \ mm$ between the piston and the cylinder wall. If the internal diameter of the cylinder is $15 \ cm$,what is the temperature at which the piston will fit into the cylinder exactly (in $^{\circ} C$)? $(\alpha_p = 1.6 \times 10^{-5} /^{\circ} C$ and $\alpha_c = 1.2 \times 10^{-5} /^{\circ} C)$

Two marks on a glass rod $10 \ cm$ apart are found to increase their distance by $0.08 \ mm$ when the rod is heated from $0 \ ^\circ C$ to $100 \ ^\circ C$. $A$ flask made of the same glass as that of the rod measures a volume $1000 \ cc$ at $0 \ ^\circ C$. The volume it measures at $100 \ ^\circ C$ in $cc$ is: