If the interatomic spacing in a steel wire is $3.0 \mathring{A}$ and $Y_{\text{steel}} = 20 \times 10^{10} \text{ N/m}^2$, then the force constant is:

$A$ wire extends by $1 \ mm$ when a force is applied. If double the force is applied to another wire of the same material and length but half the radius of the cross-section,what will be the elongation of the wire in $mm$?

If in case $A$,the elongation in a wire of length $L$ is $l$,then for the same wire,the elongation in case $B$ will be:

$A$ $5\, m$ long aluminium wire $(Y = 7 \times 10^{10}\, N/m^2)$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times 10^{10}\, N/m^2)$ of the same length under the same weight,the diameter should now be,in $mm$.

$A$ rod $BC$ of negligible mass is fixed at end $B$ and connected to a spring at its natural length having spring constant $K = 10^4 \ N/m$ at end $C$,as shown in the figure. For the rod $BC$,length $L = 4 \ m$,area of cross-section $A = 4 \times 10^{-4} \ m^2$,Young's modulus $Y = 10^{11} \ N/m^2$ and coefficient of linear expansion $\alpha = 2.2 \times 10^{-4} \ K^{-1}$. If the rod $BC$ is cooled from temperature $100^oC$ to $0^oC$,then find the decrease in length of the rod in centimeters (closest to the integer).

Two wires of equal lengths are made of the same material. Wire $A$ has a diameter that is twice as that of wire $B$. If identical weights are suspended from the ends of these wires,the increase in length is