If the breaking force for a given wire is $F$, and the thickness of the wire is doubled, then the breaking force will be:

$A$ substance breaks down by a stress of $10^6 \ N/m^2$. If the density of the material of the wire is $3 \times 10^3 \ kg/m^3$,then the length of the wire of the substance which will break under its own weight when suspended vertically,is ......... $m$.

Two strips of metal are riveted together at their ends by four rivets,each of diameter $6.0\; mm$. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed $6.9 \times 10^{7}\; Pa$? Assume that each rivet is to carry one quarter of the load.

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

$A$ string $AB$ of unstretched length $L$ is stretched by applying a force $F$ at the mid-point $C$ such that the segments $AC$ and $BC$ make an angle $\theta$ with $AB$ as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio $K$. The force $F$ is given by

$A$ 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 ......... $kg$.