$A$ wire of length $L$ is hanging from a fixed support. The length changes to $L_{1}$ and $L_{2}$ when masses $1 \, kg$ and $2 \, kg$ are suspended respectively from its free end. Then the value of $L$ is equal to:

$A$ 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 ....... .

One end of a steel rod of radius $10.0 \ mm$ and length $50.0 \ cm$ is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude $10.0 \times \pi \ kN$. This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus $= 2.0 \times 10^{11} \ N/m^2$) (in $mm$)

Which coefficient of elasticity is responsible for the propagation of a wave in a string?

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

The Young's modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section,one of steel and another of brass,are suspended from the same roof. If we want the lower ends of the wires to be at the same level,then the weights added to the steel and brass wires must be in the ratio of