Young's modulus of a material has the same units as

An area of cross-section of a rubber string is $2 \, cm^2$. Its length is doubled when stretched with a linear force of $2 \times 10^5 \, dynes$. The Young's modulus of the rubber in $dyne/cm^2$ will be:

Two metal wires $A$ and $B$ have lengths $L$ and $3L$ respectively. The radii of the cross-sectional circular areas of wires $A$ and $B$ are $R$ and $2R$,respectively. These wires are joined end-to-end along their axis. When one end of the combined system is fixed and the other end is pulled with a constant force $F$,the elongation in both wires is equal. If $Y_A$ and $Y_B$ are the Young's moduli of wires $A$ and $B$,respectively,then the ratio $Y_B / Y_A$ is:

Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is $2 \,cm$,then how much is the elongation in steel and copper wire respectively? Given,$Y_{\text{steel}} = 20 \times 10^{11} \,dyne/cm^2$,$Y_{\text{copper}} = 12 \times 10^{11} \,dyne/cm^2$.

$A$ wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $F$,its length increases by $5\,cm$. Another wire of the same material of length $4L$ and radius $4r$ is pulled by a force $4F$ under the same conditions. The increase in length of this wire is $....cm$.

$A$ steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. $A$ force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N/m^2$. The longitudinal strain produced in the wire is $..........\times 10^{-5}$.