A steel tape is calibrated at $20^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$, percentage error in the tape will be ........... $\%$ $\left[\alpha_{\text {steel }}=1.2 \times 10^{-5}{ }^{\circ} C ^{-1}\right]$

A glass flask of volume $200 \,cm ^3$ is just filled with mercury at $20^{\circ} C$. The amount of mercury that will overflow when the temperature of the system is raised to $100^{\circ} C$ is ........ $cm ^3$ $\left(\gamma_{\text {glase }}=1.2 \times 10^{-5} / C ^{\circ}, \gamma_{\text {mercury }}=1.8 \times 10^{-4} / C^{\circ}\right)$

Show that the coefficient of area expansion, $(\Delta A / A) / \Delta T,$ of a rectangular sheet of the solid is twice its Iinear expansivity, $\alpha_{1}$

The length of a metallic rod is $5m$ at $0°C$ and becomes $  5.01\, m$, on heating upto $100°C$. The linear expansion of the metal will be

A rod is placed on a smooth horizontal surface. The stress developed when temperature is increased by $40\,^oC$

$[\alpha = 5\, \times\, 10^{-5}\,^oC^{-1},\,\, \gamma = 5\, \times\, 10^{11}\,\, N/m^2]$

Two different wires having lengths $L _{1}$ and $L _{2}$ and respective temperature coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2},$ are joined end-to-end. Then the effective temperature coefficient of linear expansion is