$A$ crystal has a coefficient of linear expansion $13 \times 10^{-7} \ K^{-1}$ in one direction and $231 \times 10^{-7} \ K^{-1}$ in every direction at right angles to it. Then the cubical coefficient of expansion is:

$A$ cuboid $ABCDEFGH$ is anisotropic with $\alpha_x = 1 \times 10^{-5} /^{\circ}C$,$\alpha_y = 2 \times 10^{-5} /^{\circ}C$,$\alpha_z = 3 \times 10^{-5} /^{\circ}C$. The coefficient of superficial expansion of the faces can be:

$A$ piece of metal has a weight of $49 \ gm$ in air and $39 \ gm$ in a liquid of density $1.2 \times 10^3 \ kg/m^3$ kept at $32^{\circ}C$. When the temperature of the liquid is raised to $42^{\circ}C$, the metal piece has a weight of $40 \ gm$. If the density of the liquid at $42^{\circ}C$ is $1.0 \times 10^3 \ kg/m^3$, then the coefficient of linear expansion of the metal is:

$A$ hole is drilled in a metal sheet. At $27^{\circ}C$,the diameter of the hole is $5\,cm$. When the sheet is heated to $177^{\circ}C$,the change in the diameter of the hole is $d \times 10^{-3}\,cm$. The value of $d$ will be $...........$ if the coefficient of linear expansion of the metal is $1.6 \times 10^{-5} /^{\circ}C$.

When the temperature of a metal wire is increased from $0^{\circ} \,C$ to $10^{\circ} \,C$,its length increases by $0.02 \%$. The percentage change in its mass density will be closest to: (in $\%$)

$A$ 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 $cm$)