$A$ steel wire of diameter $2 \,mm$ has a breaking strength of $4 \times 10^5 \,N$. What is the breaking force in $\times 10^5 \,N$ for a similar steel wire of diameter $1.5 \,mm$?

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

Two blocks of masses $1 \, kg$ and $2 \, kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 \, N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 \, m/s^2$.

$A$ rod of length $1.05 \; m$ having negligible mass is supported at its ends by two wires of steel (wire $A$) and aluminium (wire $B$) of equal lengths as shown in Figure. The cross-sectional areas of wires $A$ and $B$ are $1.0 \; mm^{2}$ and $2.0 \; mm^{2}$ respectively. At what point along the rod should a mass $m$ be suspended in order to produce $(a)$ equal stresses and $(b)$ equal strains in both steel and aluminium wires?

If the breaking stress of a wire is $3.18 \times 10^{10} \, N/m^2$,what should be its minimum radius so that the wire does not break? (Refer to the figure for the masses attached to the pulley system,assume $g = 10 \, m/s^2$)

If the length of a wire is reduced to half,then it can hold the ......... load.