$A$ uniform metal bar of length $10 \ m$ with a crack at its midpoint is clamped between two rigid supports. The bar buckles upward due to a temperature rise of $40^{\circ} C$. If the coefficient of linear expansion of the metal is $2.5 \times 10^{-6} {}^{\circ} C^{-1}$,the maximum displacement of the midpoint of the bar is: (in $cm$)

$A$ non-isotropic solid metal cube has coefficients of linear expansion as:
$5 \times 10^{-5} /^{\circ} C$ along the $x$-axis and $5 \times 10^{-6} /^{\circ} C$ along the $y$ and the $z$-axis. If the coefficient of volume expansion of the solid is $C \times 10^{-6} /^{\circ} C$,then the value of $C$ is:

The side of a copper cube is $1 \ m$ at $0^{\circ} C$. What will be the change in its volume,when it is heated to $100^{\circ} C$? $[\alpha_{\text{copper}} = 18 \times 10^{-6} /^{\circ} C]$

$A$ 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:

$A$ copper rod of length $l_1$ and an iron rod of length $l_2$ are always maintained at the same common temperature $T$. If the difference $(l_2 - l_1)$ is $15\,cm$ and is independent of the value of $T$,then $l_1$ and $l_2$ have the values (given the linear coefficients of expansion for copper and iron are $\alpha_c = 2.0 \times 10^{-6}\,^{\circ}C^{-1}$ and $\alpha_i = 1.0 \times 10^{-6}\,^{\circ}C^{-1}$ respectively).

If the length of a cylinder on heating increases by $2\%$,the area of its base will increase by ....... $\%$