The atoms in solids are held together by interatomic forces. the average locations of the atoms in a lattice do not change with time and lack mobility. This makes a solid rigid and becomes a cause of elasticity in solids. In some solids such as steel, the atoms are bound together by larger inter-atomic forces than in others. Thus elastic behaviour varies from solid to solid. Even fluids exhibit elasticity. All material bodies get deformed when subjected to a suitable force. The ability of a body to regain its original shape and size is called elasticity. The deforming force per unit area is called stress. The change in dimension divided by the original dimension is called strain. The three kinds of stresses are tensile stress, shearing stress and volumetric stress similarly strains too. According to Hooke's law, within the elastic limit stress is proportional to strain.
(i) Which state of matter has volume elasticity?
(ii) When we stretch a wire, we have to perform work. Why? What happens to the energy given to the wire in this process?
(iii) Define elastic limit.
(iv) Define modulus of elastcity on what factors does it depend?
(v) Why solids are more elastic and gases are least?
(vi) The ratio of radii of two wires of same material is 2 : 1. If these wires are stretched by equal force, find the ratio of stresses Produced in them.

A wire of uniform area of cross-section is suspended vertically from a rigid support through one end with the help of an attached hanger by putting different known weights in the hanger Plot a graph between stress and strain for the stretched wire is as shown.

(i) What does the portion OA of graph represent?
(ii) Which point does the elastic limit represent?
(iii) Which region represents permanent set?
(iv) Which point does represent the yield point?
(v) Which point corresponds to breaking point or breaking stress?
(vi) Draw stress-strain variation graph for elastomers.

One end of a string of length L and cross-sectional area A is fixed to a support and the other end is fixed to a bob of mass m. The bob is revolved in a horizontal circle of radius r with an angular velocity co such that the string makes an angle \(\theta\) with the vertical.

(i) Determine the angular velocity \(\omega\) of the bob.
(ii) Determine the tension T in the string.
(iii) Determine the increase in length of the string when bob is freely suspended from rigid support.
(iv) Determine the stress in the string.
(v) A metallic wire is suspended by attaching some weight to it. If \( \alpha \) is the longitudinal strain and Y is Young's modulus, find the ratio between elastic potential energy and the energy density.

When an elastic body is subjected repeatedly to the action of alternating deforming forces, its behaviour corresponds to that of less elastic bodies due to elastic fatigue. In our daily life, elastic properties are considered while designing a structure of the material. For example, the metallic parts of the machinery are never subjected to a stress beyonds elastic limit otherwise they will get permanently deformed. The thickness of the metallic rope used in the crane in order to lift a given load is decided from the knowledge of elastic limit of the material of the rope and the factor of safety. Similarly the bridges are designed in such a way that they do not bend much or break under the load of heavy traffic, force of strongly blowing wind and its own weight.
(i) What does it mean by elastic after effect?
(ii) Define elastic fatigue
(iii) Why are bridges and girders given I shape?
(iv) A hollow shaft is found to be stronger than a solid shaft made of some equal material against twisting. Explain why?
(v) Define Poisson's ratio
(vi) An elastic wire is cut to half its original length. How would it affect the maximum load that the wire can support?
(vii) Why is a spring made of steei, not of copper?
(viii) Why are the bridges declared unsafe after long use?

A thin rod of negligible mass and cross-sectional area 4 x 10^-6m^-2, suspended vertically from one end, has a length of 0.5 m at 100° C, The rod is cooled to 0° C, Young's modulus is 10¹¹ Nm^-2, Coefficient of linear expansion = 10^{- 5} K^-1 and g = 10 ms^-2.
(i) Determine the decrease in length of the rod on cooling.
(ii) What mass must be attached at the lower end of the rod so that the rod is prevented from contracting on cooling?
(iii) Determine the total energy stored in the rod.
(iv) What is origin of elastic potential energy in a stretched wire? Give its relation with Young's modulus and strain.