Question

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

To break a wire, a force of 10⁶ N/m² is required. If the density of the material is 3×10³ kg/m³, then the length of the wire which will break by its own weight will be