Professor G. S. Mehmi

Modulus of rigidity (n): It is defined as the ratio of tangential stress to shear strain. It is also called shear modulus and is denoted by η i.e.       η = Tangential stress / Shear strain If A is area of body, F is force acting on it tangentially and θ is shear angle, then modulus of rigidity is                                         η = F / Αθ SI unit of η is N / m² or Pascal (Pa) .  CGS unit of η is dyne/cm² and dimensional formula η = [ML-1 T-2] . Poisson's Ratio (σ) : When we apply deforming force on a wire of length l and radius R, this results in the increase in length of wire but decrease in radius of wire, hence two strains are produced by a single force. I.e. Poisson's Ratio (σ) =  Lateral strain /  Longitudinal strain    ...................(i) Here Longitudinal strain = Δl/l and Lateral strain = ΔR/R Put in (...

B ulk modulus of elasticity (K): It is defined as the ratio of normal stress to the volumetric strain. It is denoted by K. Its value is also different for different types of substances. K = Normal stress/Volumetric strain   ...(i) If V is volume of a sphere of surface area A and F be the force acting on it which causes the decrease in volume as ΔV then we have   Normal stress = F/A ....(ii) and Volumetric strain = - ΔV/V .....(iii) -ve sign indicates that volume decreases on increasing pressure. Put equations (ii) and (iii) in equation (i), then we get    K = (F/A)/(- ΔV/V) Or                    K =  - FV/A ΔV ........(iv) Also we know that pressure i.e p = F/A Put in (iv) equation, then we get                           K = (- pV/ ΔV) SI unit of K is N / m² or Pascal (Pa) .  CGS unit of K is dyne/cm² and dimensional formu...

Young's modulus of elasticity (Y) = It is defined as the ratio of normal stress to the longitudinal strain. It is represented by Y and its value is different for different types of materials. Y = Normal stress / Longitudinal strain ..(1) If F is applied force and A is area of wire or body, then Normal stress =  F/A  .....(2) If L is length of wire and I(small)is increase in length of wire, then Longitudinal strain = l/L ....(3) Put equations (2) and (3) in equation (1),  we get    Y = (F / A)/(l / L) Or            Y = (FL)/(AI) SI unit of Y is N / m² or Pascal (Pa) . CGS unit of Y is dyne/cm² and dimensional formula Y = [ML-1 T-2].

Explanation of Curve : (a) P roportional limit : The portion OP of the stress-strain graph is a straight line showing that Hook's law is obeyed i.e. stress is directly proportional to the strain. The point P is called proportional limit. (b) E lastic region : PE portion of graph is not a straight line. If the wire is unloaded at point E, the graph between stress and strain is obtained in reverse direction along EPO. The point E is called elastic limit. The portion of graph berween O and E is called elastic region. For this portion of graph Hook's law is not obeyed by wire.                    Stress Strain diagram (c) P ermanent set : If wire is loaded beyond the point E i.e. elastic limit, the strain increases much more rapidly than the stress, which is indicated by portion EA of the curve. If the wire is unloaded at A, the graph between stress and strain will not be along AEPO but will be along AO'. Hence, if the wire is completely u...