$A$ thin copper wire of length $l$ metre increases in length by $2\%$ when heated through $10^{\circ}C$. The percentage increase in area when a square copper sheet of side $l$ metre is heated through $10^{\circ}C$ is:

$A$ silver rod of $100 \; cm$ at $0^{\circ} C$ is heated to $100^{\circ} C$. Its length increases by $0.19 \; cm$. The coefficient of cubical expansion of the silver rod is:

Two rods,one of aluminium and the other of steel,having initial lengths $L_1$ and $L_2$ are connected together to form a single rod of length $(L_1+L_2)$. The coefficients of linear expansion of aluminium and steel are $\alpha_1$ and $\alpha_2$ respectively. If the length of each rod increases by the same amount,when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1}{L_1+L_2}$ will be

Two holes of unequal diameters $d_1$ and $d_2$ $(d_1 > d_2)$ are cut in a metal sheet. If the sheet is heated,what happens to the diameters?

$A$ large steel wheel is to be fitted onto a shaft of the same material. At $27^{\circ}C$,the outer diameter of the shaft is $8.70\;cm$ and the diameter of the central hole in the wheel is $8.69\;cm$. The shaft is cooled using 'dry ice'. At what temperature (in $^{\circ}C$) of the shaft does the wheel slip on the shaft? Assume the coefficient of linear expansion of the steel to be constant over the required temperature range: $\alpha_{steel} = 1.20 \times 10^{-5}\;K^{-1}$.

When the temperature of a body increases from $T$ to $T+\Delta T$,its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body,then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).