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 $\alpha = 1.0 \times 10^{-5} / ^{\circ}C$)

Two brass rods $A$ and $B$ have lengths $l$ and $2l$ and radii $2r$ and $r$ respectively. If both are heated to the same temperature,the ratio of the increase in their volumes is:

$A$ glass flask contains some mercury at room temperature. It is found that at different temperatures the volume of air inside the flask remains the same. If the volume of mercury in the flask is $300 \, cm^3$,then the volume of the flask is ........ $cm^3$. (Given that the coefficient of volume expansion of mercury is $\gamma_{Hg} = 1.8 \times 10^{-4} (^{\circ}C)^{-1}$ and the coefficient of linear expansion of glass is $\alpha_{glass} = 9 \times 10^{-6} (^{\circ}C)^{-1}$)

$A$ rod is found to be $0.05 \ cm$ longer at $40^{\circ} C$ than it is at $10^{\circ} C$. The length of the rod at $0^{\circ} C$ is (coefficient of linear expansion of the material of the rod $= 1.5 \times 10^{-5} \ {}^{\circ} C^{-1}$) (in $cm$)

$A$ 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 .......... $\times 10^3 \,N$.

$A$ sheet of steel at $20^{\circ} C$ has dimensions as shown in the figure. If the coefficient of linear expansion for steel is $10^{-5} {^{\circ} C}^{-1}$, what is the change in the area at $60^{\circ} C$ (in $\text{ cm}^2$)?