The density of a rubber cord is $d$. $A$ thick rubber cord of length $L$ and cross-sectional area $A$ undergoes elongation under its own weight when suspended vertically. This elongation is proportional to:

$A$ steel ring of radius $r$ and cross-section area $A$ is fitted onto a wooden disc of radius $R$ $(R > r)$. If Young's modulus is $E$,then the force with which the steel ring is expanded is

What is the percentage increase in length of a wire of diameter $2.5 \,mm$,stretched by a force of $100 \,kg$ wt? (Young's modulus of elasticity of wire $= 12.5 \times 10^{11} \,dyne/cm^2$)

$A$ load of $1 \,kg$ weight is attached to one end of a steel wire of area of cross-section $3 \,mm^2$ and Young's modulus $10^{11} \,N/m^2$. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position, the fractional change in length is $(g = 10 \,m/s^2)$.

In the determination of Young's modulus $\left(Y=\frac{4 MLg}{\pi \ell d^2}\right)$ by using Searle's method,a wire of length $L=2 \ m$ and diameter $d=0.5 \ mm$ is used. For a load $M=2.5 \ kg$,an extension $\ell=0.25 \ mm$ in the length of the wire is observed. Quantities $d$ and $\ell$ are measured using a screw gauge and a micrometer,respectively. They have the same pitch of $0.5 \ mm$. The number of divisions on their circular scale is $100$. The contributions to the maximum probable error of the $Y$ measurement:

To double the length of an iron wire having $0.5 \, cm^2$ area of cross-section,the required force will be $(Y = 10^{12} \, dyne/cm^2)$.