An Indian rubber cord $L$ metre long and area of cross-section $A$ $m^2$ is suspended vertically. The density of rubber is $D$ $kg/m^3$ and Young's modulus of rubber is $E$ $N/m^2$. If the wire extends by $l$ metre under its own weight,then the extension $l$ is:

$A$ steel wire of length $3 \ m$ and a copper wire of length $2.2 \ m$ are connected end to end. When the combination is stretched by a force, the net elongation is $1.05 \ mm$. If the area of cross-section of each wire is $6 \ mm^2$, then the load applied is (Young's modulus of steel and copper are respectively $2 \times 10^{11} \ N/m^2$ and $1.1 \times 10^{11} \ N/m^2$) (in $N$)

If Young's modulus of iron is $2 \times 10^{11} \ N/m^2$ and the interatomic spacing between two molecules is $3 \times 10^{-10} \ m$,the interatomic force constant is ......... $N/m$.

$A$ metallic rod $1 \, cm$ long with a square cross-section is heated through $1^{\circ} C$. If Young's modulus of elasticity of the metal is $E$ and the mean coefficient of linear expansion is $\alpha$ per degree Celsius,then the compressional force required to prevent the rod from expanding along its length is: (Neglect the change of cross-sectional area)

$A$ pendulum made of a uniform wire of cross-sectional area $A$ has a time period $T$. When an additional mass $M$ is added to its bob,the time period changes to $T_M$. If the Young's modulus of the material of the wire is $Y$,then $\frac{1}{Y}$ is equal to ($g$ = gravitational acceleration).

The extension of a wire by the application of load is $3 \ mm$. The extension in a wire of the same material and length but half the radius by the same load is..... $mm$.