Related Questions

Which of the following relationships is correct for relating the three elastic constants of an isotropic elastic material (where, E = Young's modulus, G = Modulus of rigidity or shear modulus v = Poisson's ratio)?
A E = 2G (1 + v)
B E = G (1 + v)
C $${\text{E}} = \frac{{{\text{G}}\left( {1 + {\text{v}}} \right)}}{2}$$
D E = 2G (1 + 2v)
If the modulus of elasticity for a given material is twice its modulus of rigidity, then bulk modulus is equal to
A 2C
B 3C
C $$\frac{{2{\text{C}}}}{3}$$
D $$\frac{{3{\text{C}}}}{2}$$
The relation between Young's modulus (E), shear modulus (C) and bulk modulus (K) is given by
A $${\text{E}} = \frac{{3{\text{KC}}}}{{3{\text{K}} + {\text{C}}}}$$
B $${\text{E}} = \frac{{6{\text{KC}}}}{{3{\text{K}} + {\text{C}}}}$$
C $${\text{E}} = \frac{{9{\text{KC}}}}{{3{\text{K}} + {\text{C}}}}$$
D $${\text{E}} = \frac{{12{\text{KC}}}}{{3{\text{K}} + {\text{C}}}}$$
The ratio of shear modulus to the modulus of elasticity for a poisson's ratio of 0.4 will be
A 14/5
B 7/5
C 5/14
D 5/7
The stiffness of a closely coiled helical spring subjected to an axial load W is equal to (where G = Modulus of rigidity and n = Number of active coils)
A $$\frac{{{\text{G}}{{\text{d}}^4}}}{{8{{\text{D}}^3}{\text{n}}}}$$
B $$\frac{{{\text{G}}{{\text{d}}^3}}}{{8{{\text{D}}^3}{\text{n}}}}$$
C $$\frac{{{\text{G}}{{\text{d}}^4}}}{{4{{\text{D}}^3}{\text{n}}}}$$
D $$\frac{{{\text{G}}{{\text{d}}^4}}}{{8{{\text{D}}^2}{\text{n}}}}$$
When a closely-coiled helical spring of mean diameter (D) is subjected to an axial load (W), the deflection of the spring ($$\delta $$) is given by (where d = Diameter of spring wire, n = No. of turns of the spring and C = Modulus of rigidity for the spring material)
A $$\frac{{{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{C}}{{\text{d}}^4}}}$$
B $$\frac{{2{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{C}}{{\text{d}}^4}}}$$
C $$\frac{{4{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{C}}{{\text{d}}^4}}}$$
D $$\frac{{8{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{C}}{{\text{d}}^4}}}$$
The ratio of plastic section modulus to elastic section modulus
A Is equal to 1
B Is always less than 1
C Is always greater than 1
D Can be less than 1
Young's modulus may be defined as the ratio of
A Linear stress to lateral strain
B Lateral strain to linear strain
C Linear stress to linear strain
D Shear stress to shear strain
The shear modulus of most materials with respect to the modulus of elasticity is
A Equal to half
B Less than half
C More than half
D None of these
The relation between Young's modulus (E) and bulk modulus (K) is given by
A $${\text{K}} = \frac{{3{\text{m}} - 2}}{{{\text{mE}}}}$$
B $${\text{K}} = \frac{{{\text{mE}}}}{{3{\text{m}} - 2}}$$
C $${\text{K}} = \frac{{3\left( {{\text{m}} - 2} \right)}}{{{\text{mE}}}}$$
D $${\text{K}} = \frac{{{\text{mE}}}}{{3\left( {{\text{m}} - 2} \right)}}$$

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