$A$ pendulum clock shows the correct time at $20\,^oC$. The coefficient of linear expansion of the pendulum material is $12 \times 10^{-6}\,^oC^{-1}$. How much time in $sec/day$ will it lose at $40\,^oC$?

Two holes of unequal diameters $d_1$ and $d_2$ $(d_1 > d_2)$ are cut in a metal sheet. If the sheet is heated,what happens to the diameters?

$A$ uniform copper rod of length $50 \,cm$ and diameter $3.0 \,mm$ is kept on a frictionless horizontal surface at $20^{\circ} C$. The coefficient of linear expansion of copper is $2.0 \times 10^{-5} \,K^{-1}$ and Young's modulus is $1.2 \times 10^{11} \,N/m^2$. The copper rod is heated to $100^{\circ} C$. The tension developed in the copper rod is .......... $\times 10^3 \,N$.

$A$ pendulum clock loses $12 \ s$ a day if the temperature is $40^{\circ} C$ and gains $4 \ s$ a day if the temperature is $20^{\circ} C$. The temperature at which the clock will show the correct time is: (in $^{\circ} C$)

On what value does the coefficient of linear expansion $\alpha_l$ depend? Write its unit.

$A$ 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 $^{\circ} C$)