$A$ man grows into a giant such that his linear dimensions increase by a factor of $9$. Assuming that his density remains the same,the stress in the leg will change by a factor of

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

The density and breaking stress of a wire are $6 \times 10^4 \ kg/m^3$ and $1.2 \times 10^8 \ N/m^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}$ of the value on the surface of Earth. The maximum length of the wire without breaking is ............ $m$ (take $g = 10 \ m/s^2$ on Earth).

To break a wire,a breaking stress of $10^6 \, N/m^2$ is required. If the density of the material is $3 \times 10^3 \, kg/m^3$,then the length of the wire which will break by its own weight will be......... $m$ (Take $g = 10 \, m/s^2$)

One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration $2 \ m/s^2$ and a load of $10 \ kg$ hangs from the other end. If the cross-section of the wire is $2 \ cm^2$,then the longitudinal strain in the wire will be ($g = 10 \ m/s^2$ and $Y = 2.0 \times 10^{11} \ N/m^2$).

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	$IV$. $-\frac{\Delta D/D}{\Delta L/L}$