Draw the graph of the coefficient of volume expansion $(\alpha_V)$ versus temperature $(T)$ for a solid.

If a cylinder of diameter $1.0 \, cm$ at $30^{\circ}C$ is to be slid into a hole of diameter $0.9997 \, cm$ in a steel plate at the same temperature,then the minimum required rise in the temperature of the plate is ........ $^{\circ}C$ (Coefficient of linear expansion of steel $\alpha = 12 \times 10^{-6} \, ^{\circ}C^{-1}$).

The coefficient of linear expansion of a crystalline substance in one direction is $2 \times 10^{-4} /{ }^{\circ} C$ and in every direction perpendicular to it is $3 \times 10^{-4} /{ }^{\circ} C$. The coefficient of cubical expansion of the crystal is equal to ........... $\times 10^{-4} /{ }^{\circ} C$.

When a copper ball is heated,the largest percentage increase will occur in its

$A$ circular copper ring at $30^{\circ} C$ has a hole with an area of $9.98 \ cm^2$. It is made to slip onto a steel rod of cross-sectional area of $10 \ cm^2$, by raising the temperature of both the ring and the rod simultaneously by an amount $\Delta T$. If the coefficients of linear expansion of copper and steel are $17 \times 10^{-6} /{ }^{\circ} C$ and $11 \times 10^{-6} /{ }^{\circ} C$ respectively, then the minimum value of $\Delta T$ should be: (in $^{\circ} C$)

When a bimetallic strip is heated, it . . . . . . .