$A$ 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 $g = 10 \, m/s^2$)

In a series combination of copper and steel wires of same length and same diameter,a force is applied at one of their ends while the other end is kept fixed. The combined length is increased by $2 \ cm$. The wires will have ..........

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

Potassium has a $bcc$ structure with a nearest neighbour distance of $4.525 \ \mathring{A}$. Its atomic weight is $39$. Its density in $kg/m^{3}$ is:

$A$ 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

One end of a wire of $8 \,mm$ radius and $100 \,cm$ length is fixed and the other end is twisted through an angle of $45^{\circ}$. The angle of shear is (in $^{\circ}$)