Match the following:

Column $I$	Column $II$
$A$. Hooke's law	$1$. Tangential strain
$B$. Shearing strain	$2$. Temporary loss of elastic property
$C$. Bulk strain	$3$. Elastic limit
$D$. Elastic fatigue	$4$. $3$ times the linear strain

$A$ metal rod of cross-sectional area $10^{-4} \, m^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \, K^{-1}$ and its Young's modulus is $4 \times 10^{12} \, N/m^{2}$. When the temperature of the chamber is lowered to $T$,a weight of $5000 \, N$ needs to be attached to the rod so that its length remains unchanged. Then,$T$ is ............ $^{\circ} C$.

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. Young's Modulus	$I$. $\frac{Ad}{\Delta L}$
$B$. Compressibility	$II$. $\frac{FL}{A\Delta L}$
$C$. Bulk Modulus	$III$. $-\frac{1}{\Delta P}(\frac{\Delta V}{V})$
$D$. Poisson's Ratio	$IV$. $-\frac{\Delta D/D}{\Delta L/L}$

$A$ wire of density $3 \times 10^3 \, kg/m^3$ requires a breaking stress of $10^6 \, N/m^2$ to break. What should be the length of the wire so that it breaks under its own weight? (Take $g = 10 \, m/s^2$)

$A$ wire of length $5 \,m$ is twisted through $30^{\circ}$ at its free end. If the radius of the wire is $1 \,mm$,the shearing strain in the wire is: (in $^{\circ}$)

$A$ steel wire can sustain $100\,kg$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of ......... $kg$.