$A$ pendulum clock shows the correct time at $20\,^oC$. The coefficient of linear expansion of the pendulum material is $12 \times 10^{-6}\,^oC^{-1}$. How much time in $sec/day$ will it lose at $40\,^oC$?

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,then:

Solids expand on heating because

The ratio of linear expansivity to the coefficient of superficial expansion of a rectangular sheet of a solid is

$A$ 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 $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).

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