What is the change in volume of an iron sphere of volume $500 \,cm^3$, when it is heated from $0^{\circ} C$ to $100^{\circ} C$ (in $\,cm^3$)? (Given: $\alpha_{\text{Iron}} = 12 \times 10^{-6} /^{\circ} C$)

$A$ blacksmith fixes a circular iron frame on the wooden wheel of a bullock cart. The diameters of the wooden wheel and the circular iron frame are $5.012 \ m$ and $5 \ m$ respectively at $27^{\circ} C$. The temperature (in $^{\circ} C$) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).

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 per $^{\circ}C^{-1}$) of the metal is :-

If two rods of length $L$ and $2L$ having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected so that the total length becomes $3L$,the average coefficient of linear expansion of the composite rod equals:

The moment of inertia $I$ of a uniform rod about a perpendicular bisector increases to $I+\Delta I$, if the temperature is increased slightly by $\Delta T$. If the coefficient of linear expansion is $\alpha$, then $\frac{\Delta I}{I}$ is (Assume $\frac{\Delta T}{T} \ll 1$)

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