Question

The stress-strain curves vary from material to material. These curves help us to understand how a given material deforms with increasing loads. From the graph, we can see that in the region between O to A, the curve is linear. In this region, Hooke's law is obeyed. The body regains its original dimensions when the applied force is removed. In this region, the solid behaves as an elastic body.

A bridge must be designed such that it can withstand the load of the flowing traffic, the force of winds and its own weight. Similarly, in the design of buildings the use of beams and columns is very common. In both the cases, the overcoming of the problem of bending of beam under a load is of prime importance. The beam should not bend too much or break. A bar of length l, breadth b, and depth d when loaded at the centre by a load W sags by an amount given by δ = Wl3/(4bd3Y)

The ratio of stress and strain, called modulus of elasticity, is found to be a characteristic of the material. Experimental observation shows that for a given material, the magnitude of the strain produced is same whether the stress is tensile or compressive. The ratio of tensile (or compressive) stress (σ) to the longitudinal strain (ε) is defined as Young's modulus and is denoted by the symbol Y. Y = Stress (σ)/Strain (ε) = (F/A)/(ΔL/L) = F × L/(A × ΔL) Since strain is a dimensionless quantity, the unit of Young's modulus is the same as that of stress i.e., N m-2 or Pascal (Pa)

An Indian rubber cord L metre long and area of cross-section A meter² is suspended vertically. Density of rubber is D kg/m³ and Young's modulus of rubber is E N/m². If the wire extends by l metre under its own weight, then extension l is