Elasticity PYQs - Last 5 Years

There are two wires of same material and same length while the diameter of second wire is two times the diameter of the first wire. Then the ratio of extensions produced in the wires by applying same load will be

Two wires A and B are made of same material. Their diameters are in the ratio of $1: 2$ and lengths are in the ratio of $1: 3$. If they are stretched by the same force, then increase in their lengths will be in the ratio of

A thick metal wire of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the wire due to its own weight is ( $Y=$ Young's modulus of the material of the wire)

A stretched wire of a material whose young's modulus \(Y=2 \times 10^{11} ~\mathrm{Nm}^{-2}\) has poisson's ratio 0.25 . Its lateral strain \(\varepsilon_l=10^{-3}\). The elastic energy density of the wire is

A metallic rod breaks when strain produced is \(0.2 \%\). The Young's modulus of the material of the \(\operatorname{rod} 7 \times 10^9 \mathrm{~N} / \mathrm{m}^2\). The area of crosssection to support a load of \(10^4 \mathrm{~N}\) is