The elongation of the copper wire of cross-sectional area $3.5 \,mm^2$, as shown in the figure, is (Given: $Y_{\text{copper}} = 10 \times 10^{10} \,N/m^2$ and $g = 10 \,m/s^2$).

$A$ rigid massless rod of length $6L$ is suspended horizontally by means of two elastic rods $PQ$ and $RS$ as shown in the figure. Their area of cross-section,Young's modulus,and lengths are mentioned in the figure. Find the deflection of end $S$ in the equilibrium state. The free end of the rigid rod is pushed down by a constant force $F$. $A$ is the area of cross-section,$Y$ is Young's modulus of elasticity.

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$,the force with which the metal ring expands is

Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths,radii,and Young's modulus of wires $A$ and $B$ are $r, 2r$,and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if the ratio of the increase in their corresponding lengths is $1/(6r^2)$. The mass of block $Q$ is $3M$.

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)