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

Same tension is applied to the following four wires made of same material. The elongation is longest in

$A$ steel rail of length $5\,m$ and area of cross-section $40\,cm^2$ is prevented from expanding along its length while the temperature rises by $10\,^{\circ}C$. If the coefficient of linear expansion and Young's modulus of steel are $1.2\times10^{-5}\,K^{-1}$ and $2\times10^{11}\,N/m^2$ respectively,the force developed in the rail is approximately:

$A$ steel rod has a radius of $50 \ mm$ and a length of $2 \ m$. It is stretched along its length with a force of $400 \ kN$. This causes an elongation of $0.5 \ mm$. Find the (approximate) Young's modulus of steel from this information.

One end of the steel rod is clamped to the roof and the other end is attached to a mass of $1000 \,kg$ as shown in the figure. The length of the rod is $50 \,cm$ and its cross-sectional area is $1000 \,mm^2$. The change in the length of the rod due to the weight of the mass is (Young's modulus of steel $= 2 \times 10^{11} \,Nm^{-2}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,mm$)

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