Mechanical Properties of Solids Test

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Mechanical Properties of Solids Test - 3

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Question 1
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According to Hooke’s law

A
For small deformations the stress and strain are inversely proportional to each other

B
For small deformations the stress and strain are proportional to each other

C
For small deformations the stress is proportional to square of strain

D
For large deformations the stress and strain are proportional to each other

Solution

By definition of Hooke's law
within elastic limit, the stress developed is directly proportional to the strain produced in a body.
stress ∝ strain
Question 2
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Elastomers are materials

A
which can be stretched to cause large strains

B
which cannot be stretched to beyond elastic limit

C
which cannot be stretched to cause large strains

D
which can be stretched without corresponding stress

Solution

Substances like tissue of aorta (Present in the heart), rubber etc. which can be stretched to cause large strains are called elastomers. They show large plastic range in stress-strain curve.
Question 3
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Young’s modulus Y is

A
the ratio of shear stress (σ) to the longitudinal strain (θ)

B
the ratio of longitudinal strain (ε) to the tensile (or compressive) stress (σ)

C
the ratio of shear strain (θ) to the longitudinal stress (σ)

D
the ratio of tensile (or compressive) stress (σ) to the longitudinal strain (ε)

Solution

The ratio of stress and strain is called modulus of elasticity is the characteristic of the material. they are (a) Young's modulus (b) Shear Modulus (c) Bulk modulus

Young's Modulus is denoted by Y and is given by the ratio of tensile (or compressive) stress (σ) to the longitudinal strain (ε)

Y = tensile stress/longitudinal strain

Y=σ/ϵ
Question 4
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Shear modulus or modulus of rigidity is

A
the ratio of shearing strain to the corresponding shearing stress

B
the ratio of longitudinal stress to the corresponding shearing strain

C
the ratio of shearing stress to the corresponding shearing strain

D
the ratio of shearing stress to the corresponding lateral strain

Solution

The ratio of shearing stress to the corresponding shearing strain is called the shear modulus of the material and is represented by G. It is also called the modulus of rigidity.
G = shearing stress(σ) / shearing strain
Question 5
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Bulk modulus is

A
the ratio of longitudinal stress to the corresponding hydraulic strain

B
the ratio of hydraulic strain to the corresponding hydraulic stress

C
the ratio of lateral stress to the corresponding hydraulic strain

D
the ratio of hydraulic stress to the corresponding hydraulic strain

Solution

When a body is submerged in a fluid, it undergoes a hydraulic stress (equal in magnitude to the hydraulic pressure). This leads to the decrease in the volume of the body thus producing a strain called volume strain. The ratio of hydraulic stress to the corresponding hydraulic strain is called bulk modulus. It is denoted by symbol B.

Hence, bulk modulus = hydraulic or normal stress/ volumetric strain

B = −p / (δV / V)

The negative sign indicates the fact that with an increase in pressure, a decrease in volume occurs.