$A$ steel wire of $1 \, m$ long and $1 \, mm^2$ cross-sectional area is hung from a rigid support. When a weight of $1 \, kg$ is hung from it,the change in length will be given by ..... $mm$ $(Y = 2 \times 10^{11} \, N/m^2, g = 10 \, m/s^2)$.

$A$ student performs an experiment to determine the Young's modulus of a wire, exactly $2 \,m$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \,mm$ with an uncertainty of $\pm 0.05 \,mm$ at a load of exactly $1.0 \,kg$. The student also measures the diameter of the wire to be $0.4 \,mm$ with an uncertainty of $\pm 0.01 \,mm$. Take $g=9.8 \,m/s^2$ (exact). The Young's modulus obtained from the reading is

$A$ 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.

$A$ steel rod with $Y = 2.0 \times 10^{11} \, N/m^2$ and $\alpha = 10^{-5} \, ^\circ C^{-1}$ of length $4 \, m$ and area of cross-section $10 \, cm^2$ is heated from $0^\circ C$ to $400^\circ C$ without being allowed to extend. The tension produced in the rod is $x \times 10^5 \, N$ where the value of $x$ is ....... .

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$,how much force is needed to stretch the second wire by the same amount?

The area of a cross-section of a steel wire is $0.1 \, cm^2$ and Young's modulus of steel is $2 \times 10^{11} \, N \, m^{-2}$. The force required to stretch it by $0.1 \%$ of its original length is ......... $N$.