The scale on a steel metre stick is calibrated at $20^{\circ}C$. The error in the reading of $50 \, cm$ at $30^{\circ}C$ is: (take linear expansion coefficient of steel $\alpha = 1.0 \times 10^{-5} / ^{\circ}C$)

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20\,^{\circ}C$,the coefficient of linear expansion (in $^{\circ}C^{-1}$) of the metal is

$A$ 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 $\alpha = 1.70 \times 10^{-5} \; K^{-1}$)

The difference in length between two rods $A$ and $B$ is $60 \ cm$ at all temperatures. If $\alpha_A = 18 \times 10^{-6} /^{\circ}C$ and $\alpha_B = 27 \times 10^{-6} /^{\circ}C$,then the lengths of rod $A$ and rod $B$ at $0^{\circ}C$ are respectively:

The area of cross-section of a railway track is $0.01\, m^2$. The temperature variation is $10^{\circ}C$. The coefficient of linear expansion of the material of the track is $10^{-5} /^{\circ}C$. The energy stored per meter in the track is ...... $J/m$. (Young's modulus of the material of the track is $10^{11}\, Nm^{-2}$)

The temperature of a metal coin is increased by $100^{\circ} C$ and its diameter increases by $0.15 \%$. Its area increases by nearly (in $\%$)