One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If $A$ is the area of cross-section of the wire,the stress in the wire at a height $3L/4$ from its lower end is

There is some change in length when a $33000 \,N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \,m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} \,N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ}C$). (in $^{\circ}C$)

$A$ wire of cross-sectional area $10^{-6} \, m^2$ is stretched such that its length increases by $0.1\%$. If the tension produced in the wire is $1000 \, N$, calculate the Young's modulus of the wire.

$A$ meter scale of mass $m$,Young's modulus $Y$,and cross-sectional area $A$ is hung vertically from the ceiling at the zero mark. The separation between the $30\ cm$ and $70\ cm$ marks will be: (Assume $\frac{mg}{AY}$ is dimensionless)

Increase in length of a wire is $1 \, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius,the increase in length will be ........ $mm$.

Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by forces in the ratio $3: 1$. The ratio of the elastic potential energies stored per unit volume in the wires $A$ and $B$ is