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 $\alpha = 12 \times 10^{-6} \, ^{\circ}C^{-1}$).

$A$ hole is drilled in a copper sheet. The diameter of the hole is $4.24 \; cm$ at $27.0 \; ^{\circ}C$. What is the change in the diameter of the hole when the sheet is heated to $227 \; ^{\circ}C$? (Coefficient of linear expansion of copper $\alpha = 1.70 \times 10^{-5} \; K^{-1}$)

$A$ piece of metal has a weight of $49 \ gm$ in air and $39 \ gm$ in a liquid of density $1.2 \times 10^3 \ kg/m^3$ kept at $32^{\circ}C$. When the temperature of the liquid is raised to $42^{\circ}C$, the metal piece has a weight of $40 \ gm$. If the density of the liquid at $42^{\circ}C$ is $1.0 \times 10^3 \ kg/m^3$, then the coefficient of linear expansion of the metal is:

An iron rod has a length of $10 \ cm$ at $20^{\circ}C$. What will be the change in length of the iron rod at $19^{\circ}C$? (Given for iron,$\alpha = 11 \times 10^{-6} \ ^{\circ}C^{-1}$)

At a certain temperature,rod $A$ and rod $B$ of different materials have lengths $L_A$ and $L_B$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $L_A / L_B$ is given by

$A$ 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 correct time,and the coefficient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively: