$A$ steel tape of $300 \,cm$ length is graduated at $27^{\circ} C$. The length of a steel rod measured using the tape is found to be $110 \,cm$ at $50^{\circ} C$. The actual length of the steel rod at $50^{\circ} C$ is $(\alpha_{\text{steel}} = 1.2 \times 10^{-5} \,K^{-1})$. (in $\,cm$)

When a copper ball is heated,which of the following will show the maximum percentage increase?

$A$ pendulum clock keeps correct time at $0\,^{\circ}C$. The thermal coefficient of linear expansion of the material of the pendulum is $\alpha$. If the temperature rises to $t\,^{\circ}C$,then the clock loses per day by (in seconds):

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?

$A$ crystal has a linear expansion coefficient of $\alpha_1$ in one direction and $\alpha_2$ in all directions perpendicular to it. What will be the volume expansion coefficient of the crystal?

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