If E, G and K denote Young’s modulus of elasticity, Modulus of rigidity and Bulk modulus, respectively, for an elastic material then which one of the following can be possibly true?

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

$$\frac{{3{\text{C}}}}{2}$$

If E, N, K and $$\frac{1}{{\text{m}}}$$ are modulus of elasticity, modulus of rigidity. Bulk modulus and Poisson ratio of the material, the following relationship holds good

A

$${\text{E}} = 3{\text{K}}\left( {1 - \frac{2}{{\text{m}}}} \right)$$

B

$${\text{E}} = 2{\text{N}}\left( {1 + \frac{1}{{\text{m}}}} \right)$$

C

$$\frac{3}{2}{\text{K}}\left( {1 - \frac{2}{{\text{m}}}} \right) = {\text{N}}\left( {1 + \frac{1}{{\text{m}}}} \right)$$

D

All the above

Two beams PQ (fixed at P and with a roller support at Q, as shown in Figure I, which allows vertical movement) and XZ (with a hinge at Y) are shown in the Figures I and II respectively. The spans of PQ and XZ are L and 2L respectively. Both the beams are under the action of uniformly distributed load (W) and have the same flexural stiffness, EI (where, E and I respectively denote modulus of elasticity and moment of inertia about axis of bending). Let the maximum deflection and maximum rotation be δmax1 and θmax1, respectively, in the case of beam PQ and the corresponding quantities for the beam XZ be δmax2 and θmax2, respectively. Which one of the following relationships is true?

A

δ_max1 ≠ δ_max2 and θ_max1 ≠ θ_max2

B

δ_max1 = δ_max2 and θ_max1 ≠ θ_max2

C

δ_max1 ≠ δ_max2 and θ_max1 = θ_max2

D

δ_max1 = δ_max2 and θ_max1 = θ_max2

In an experiment, the bulk modulus of elasticity of a material is twice its modulus of rigidity. The Poissons ratio of the material is ___________

A

1/7

B

2/7

C

3/7

D

4/7

What is the relationship between the linear elastic properties Youngs modulus, bulk modulus and rigidity modulus?

A

1/E = 9/k + 3/G

B

9/E = 3/K + 1/G

C

3/E = 9/K + 1/G

D

9/E = 1/K + 3/G

Consider the following statements.
1. The SI unit of young's modulus of elasticity is N/M².
2. The reciprocal of the bulk modulus of the material of the body is called the compressibility of that material.
3. Compressibility of gases is very small.
Which of the statements given above are correct?

A

1, 2 and 3

B

1 and 3

C

1 and 2

D

None of these

Youngs modulus of elasticity and Poissons ratio of a material are 1.25 x 102 MPa and 0.34 respectively. The modulus of rigidity of the material is __________

A

0.9469 MPa

B

0.8375 MPa

C

0.4664 MPa

D

0.4025 MPa

Determine the Poissons ratio and bulk modulus of a material, for which Youngs modulus is 1.2 and modulus of rigidity is 4.8.

A

7

B

8

C

9

D

10

E, G, K and μ elastic modulus, shear modulus, bulk modulus and Poisson’s ratio respectively. To express the stress strain relations completely for this material, at least __________

A

E, G and μmust be known

B

E, K and μmust be known

C

Any two of the four must be known

D

All the four must be known

If E, G and K denote Young’s modulus of elasticity, Modulus of rigidity and Bulk modulus, respectively, for an elastic material then which one of the following can be possibly true?

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