The length of an elastic string is a metre when the longitudinal tension is $4\, N$ and $b$ metre when the longitudinal tension is $5\, N$. The length of the string in metre when the longitudinal tension is $9\, N$ is

The extension of a wire by the application of load is $3$ $mm.$ The extension in a wire of the same material and length but half the radius by the same load is….. $mm$

Explain with illustration cranes regarding the applications of elastic behaviour of materials.

In nature the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus, the vertical through the centre of gravity does not fall withinthe  base. The elastic torque caused because of this bending about the central axis of the tree is given by $\frac{{Y\pi {r^4}}}{{4R}}$ $Y$ is the Young’s modulus, $r$ is the radius of the trunk and $R$ is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?