$A$ seconds pendulum clock has a steel wire. The clock shows correct time at $25^{\circ} C$. How many seconds does the clock lose or gain in one week,when the temperature is increased to $35^{\circ} C$? (Given: $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /^{\circ} C$)

Two rods of same area of cross-section have lengths $L$ and $2 \,L$ and coefficients of linear expansion $2 \alpha$ and $\alpha$ respectively. If they are welded to form a composite rod of length $3 \,L$, then the coefficient of linear expansion of the composite rod is

$A$ sphere floats on a liquid whose volume does not change with temperature. At temperatures $t_1$ and $t_2$,the fractions $f_1$ and $f_2$ of the sphere are submerged in the liquid,respectively. What is the coefficient of volume expansion of the sphere?

Solids expand on heating because ................

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

Steel rails are laid with gaps to allow for thermal expansion. Each track is $10 \ m$ long,when laid at a temperature of $17^{\circ} C$. The maximum temperature that can be reached is $45^{\circ} C$. The gap to be kept between the two segments of the railway track is $(\alpha_{\text{steel}} = 1.3 \times 10^{-5} /^{\circ} C)$. (in $mm$)