A force $F$ is applied on the wire of radius $r$ and length $L$ and change in the length of wire is $l.$ If the same force $F$ is applied on the wire of the same material and radius $2r$ and length $2L,$ Then the change in length of the other wire is

A steel wire of length $4.7\; m$ and cross-sectional area $3.0 \times 10^{-5}\; m ^{2}$ stretches by the same amount as a copper wire of length $3.5\; m$ and cross-sectional area of $4.0 \times 10^{-5} \;m ^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?

A bar is subjected to axial forces as shown. If $E$ is the modulus of elasticity of the bar and $A$ is its crosssection area. Its elongation will be

Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

A uniform heavy rod of weight $10\, {kg} {ms}^{-2}$, crosssectional area $100\, {cm}^{2}$ and length $20\, {cm}$ is hanging from a fixed support. Young modulus of the material of the rod is $2 \times 10^{11} \,{Nm}^{-2}$. Neglecting the lateral contraction, find the elongation of rod due to its own weight. (In $\times 10^{-10} {m}$)