Two similar wires under the same load yield elongations of $0.1 \ mm$ and $0.05 \ mm$ respectively. If the area of cross-section of the first wire is $4 \ mm^2$,then the area of cross-section of the second wire is..... $mm^2$.

The dimensions of four wires of the same material are given below. The increase in length is maximum in the wire of

The speed of a transverse wave passing through a string of length $50 \; cm$ and mass $10 \; g$ is $60 \; ms^{-1}$. The area of cross-section of the wire is $2.0 \; mm^2$ and its Young's modulus is $1.2 \times 10^{11} \; Nm^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5} \; m$. The value of $x$ is $...$

$A$ wire of length $L$ and area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when a mass $M$ is suspended from its free end. The expression for Young's modulus is:

$A$ stress of $1.5 \, kg.wt/mm^2$ is applied to a wire of Young's modulus $5 \times 10^{11} \, N/m^2$. The percentage increase in its length is

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.