Elastic Constants

Q. The relationship between Young's Modulus E, Modulus of Rigidity C and Bulk Modulus K in an elastic material is given by the relation

1. $E=\frac{9KC}{3K+C}$
2. $E=\frac{3KC}{3K+C}$
3. $E=\frac{9KC}{9K+C}$
4. $E=\frac{3KC}{9K+C}$

Q.

Modulus of rigidity of ideal liquids is

1. infinity

2. zero

3. unity

4. some finite small non - zero

Q. In terms of bulk modulus (K) and modulus of rigidity (G), Poisson's ratio can be expressed as

1. $\frac{3K-4G}{6K+4G}$
2. $\frac{3K+4G}{6K-4G}$
3. $\frac{3K-2G}{6K+2G}$
4. $\frac{3K+2G}{6K-2G}$

Q. A bar of diameter 30 mm is subjected to a tensile load such that the measured extension on a gauge length of 200 mm is 0.09 mm and the change in diameter is 0.0045 mm. The Poisson's ratio will be

1. $1/4$
2. $1/3$
3. $1/5$
4. $1/6$

Q. A bar of 40 mm diameter and 400 mm length is subjected to an axial load of 100 kN. It elongates by 0.150 mm and the diameter decreases by 0.005 mm. What is the Poisson's ratio of the material of the bar?

1. 0.25
2. 0.28
3. 0.33
4. 0.37

Q. For a linear, elastic, isotropic material, the number of independent elastic constants is

1. $1$
2. $2$
3. $3$
4. $4$

Q. If the Young's modulus 'E' is equal to the bulk modulus 'K', then what is the value of the Poisson's ratio?

1. $1/4$
2. $1/2$
3. $1/3$
4. $3/4$

Q. The Poisson's ratio for a perfectly incompressible linear elastic material is

1. 1
2. 0.5
3. 0
4. Infinity

Q. The bulk modulus of elasticity of a material is twice its modulus of rigidity. The Poisson's ratio of the material is

1. $1/7$
2. $2/7$
3. $3/7$
4. $4/7$

Q. A bar of uniform section is subjected to axial tensile loads such that the normal strain in the direction is 1.25 mm per m. If the Poisson's ratio of the material of the bar is 0.3, the volumetric strain would be

1. $2\times {10}^{-4}$
2. $3\times {10}^{-4}$
3. $4\times {10}^{-4}$
4. $5\times {10}^{-4}$

Q. Limiting values of Poisson's ratio are:

1. - 1 and 0.5
2. - 1 and - 0.5
3. 1 and - 0.5
4. 0 and 0.5

Q. A steel cube of volume $8000cc$ is subjected to all round stress of $1330kg/c{m}^2$. The bulk modulus of the material is $1.33\times {10}^{6}kg/c{m}^2$. The volumetric change is

1. $8cc$
2. $6cc$
3. $0.8cc$
4. ${10}^{-3}cc$

Q. A given material has Young's modulus E, modulus of rigidity G and Poisson's ratio 0.25. The ratio of Young's modulus to modulus of rigidity of this material is

1. $3.75$
2. $3$
3. $2.5$
4. $1.5$

Q. A circular rod of diameter 30 mm and length 200 mm is subjected to a tensile force. The extension in rod is 0.09 mm and change in diameter is 0.0045 mm. What is the Poisson's ratio of the material of the rod ?

1. 0.30
2. 0.32
3. 0.33
4. 0.35

Q. For a given elastic material, the Elastic Modulus E is 210 GPa and its Poisson's Ratio is 0.27. What is the approximate value of its Modulus of Rigidity?

1. 105 GPa
2. 83 GPa
3. 159 GPa
4. 165 GPa

Q. The value of modulus of elasticity for a material is $200GN/m^2$ and Poisson's ratio is $0.25$. What is its modulus of rigidity?

1. $250GN/m^2$
2. $320GN/m^2$
3. $125GN/m^2$
4. $80GN/m^2$

Q. In a body loaded under plane stress conditions, what is the number of independent stress components in order to completely specify the state of stress at a point ?

1. 3
2. 4
3. 6
4. 9

Q. In an experiment it found that the bulk modulus of a material is equal to its shear modulus. The Poisson's ratio is

1. $0.125$
2. $0.250$
3. $0.375$
4. $0.500$

Q. If the Poissons's ratio of an elastic material is 0.4. The ratio of modulus of rigidity to Young's modulus is

1. 0.357

Q. Poisson's ratio of a material is 0.3. Then the ratio of Young's modulus to bulk modulus is

1. $0.6$
2. $0.8$
3. $1.2$
4. $1.4$

Q. If a material has identical elastic properties in all directions, it is said to be

1. elastic
2. isotropic
3. orthotropic
4. homogeneous

Q. If a member is subjected to tensile stress of ${}^{\prime }{p}_x^{\prime }$, compressive stress of ${}^{\prime }{p}_y^{\prime }$ and tensile stress of ${}^{\prime }{p}_z^{\prime }$, along the $X,Y$ and $Z$ directions respectively, then the resultant strain ${\epsilon }_x^{\prime }$; along the $X$ direction would be (E is Young's modulus of elasticity and 'μ' is Poisson's ratio)

1. $\frac{1}{E}(p_x+\mu p_y-\mu p_z)$
2. $\frac{1}{E}(p_x+\mu p_y+\mu p_z)$
3. $\frac{1}{E}(p_x-\mu p_y+\mu p_z)$
4. $\frac{1}{E}(p_x-\mu p_y-\mu p_z)$

Q. The side $AD$ of the square block $ABCD$ as shown in the given figure is fixed at the base and it is under a stage of simple shear causing shear stress $\tau$ and shear strain $\Phi$,
where $\Phi =\frac{\tau }{\text{Modulus of Rigidity (G)}}$
The distorted shape is $A{B}^{\prime }{C}^{\prime }D$. The diagonal strain (linear) will be

1. $\Phi /2$
2. $\Phi /\sqrt{2}$
3. $\sqrt{2}\Phi$
4. $\Phi$

Q. For a material having modulus of elasticity equal to 208 GPa and Poisson's ratio equal to 0.3, what is the modulus of rigidity ?

1. 74.0 GPa
2. 80.0 GPa
3. 100.0 GPa
4. 128.5 GPa

Q. A metallic rod of 500 mm length and 50 mm diameter when subjected to a tensile force of 100 kN at the ends, experiences an increase in its length by 0.5 mm and a reduction in its diameter by 0.015 mm. The Poisson's ratio of the rod material is

1. 0.3

Q. The longitudinal strain of a cylindrical bar of 25 mm diameter and 1.5 m length is found to be 3 times its lateral strain in a tensile test. What is the value of Bulk Modulus by assuming $E=1\times {10}^{5}N/m{m}^2?$

1. $2\times {10}^{5}N/m{m}^2$
2. $1.1\times {10}^{5}N/m{m}^2$
3. $1\times {10}^{5}N/m{m}^2$
4. $2\times {10}^{5}N/m{m}^2$

Q. Poisson's ratio is defined as the ratio of

1. longitudinal stress and longitudinal strain
2. lateral strain and longitudinal strain
3. longitudinal stress and lateral stress
4. lateral stress and longitudinal stress

Q.

The sum can be found of an infinite $G.P.$ whose common ratio is $r$

1. For all value of $r$

2. For only positive values of $r$

3. Only for $0<r<1$

4. Only for $-1<r<1(r\ne 0)$

Q. Given E as the Young's modulus of elasticity of a material, what can be the minimum value of its bulk modulus or elasticity?

1. $\frac{E}{2}$
2. $\frac{E}{3}$
3. $\frac{E}{4}$
4. $\frac{E}{5}$

Q. A rod is subjected to a uni-axial load within linear elastic limit. When the change in the stress is 200 MPa, the change in the strain is 0.001. If the Poisson's ratio of the rod is 0.3, the modulus of rigidity (in GPa) is

1. 76.923