Two wires $A$ and $B$ are of the same material. Their lengths are in the ratio $1: 2$ and diameters are in the ratio $2: 1$. When stretched by forces $F_{A}$ and $F_{B}$ respectively,they get equal increase in their lengths. Then the ratio $F_{A} / F_{B}$ is

$A$ $0.1 \,kg$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \,m$ and its cross-sectional area is $4.9 \times 10^{-7} \,m^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \,rad \,s^{-1}$. If the Young's modulus of the material of the wire is $n \times 10^9 \,N \,m^{-2}$, the value of $n$ is

If the ratio of length,radii,and Young's modulus of steel and aluminium wire are $a, b, c$ respectively,then the corresponding ratio of increase in their length would be:

Write the unit and dimensional formula of modulus of elasticity.

The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension,when the same tension is applied?

$A$ wire of length $2 \, m$ is made from copper having a volume of $10 \, cm^3$. When a force $F$ is applied,the extension in its length is $2 \, mm$. If a wire of length $8 \, m$ is made from the same volume of copper,what will be the extension in its length in $cm$ when the same force $F$ is applied?