When a shearing force is applied to a body,elastic potential energy is stored in it. Upon removing the force,this energy:

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).

$A$ uniform wire (Young's modulus $2 \times 10^{11} \, Nm^{-2}$) is subjected to a longitudinal tensile stress of $5 \times 10^7 \, Nm^{-2}$. If the overall volume change in the wire is $0.02\%$,the fractional decrease in the radius of the wire is close to:

Two blocks of masses $1 \,kg$ and $2 \,kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of metal is $\frac{40}{3 \pi} \times 10^6 \,N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $(g = 10 \,m s^{-2})$

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

$A$ bob of mass $10\, kg$ is attached to a wire $0.3\, m$ long. Its breaking stress is $4.8 \times 10^7\, N/m^2$. The area of cross-section of the wire is $10^{-6}\, m^2$. The maximum angular velocity with which it can be rotated in a horizontal circle is ....... $rad/sec$.