Mechanical Properties of Solids Test

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Mechanical Properties of Solids Test - 13

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Question 1
1 / -0

Which of the following is an example of plastic deformation?

A
stretching a rubber band

B
stretching salt water taffy

C
none

D
both

Solution

Whenever a deforming force is applied to a non-rigid substance, the substance undergoes deformation in dimension or shape. Elastic substances are those which come back to their original shape or dimensions after the deformation force is removed. Plastic substances are those which do not come back to their original shape or dimensions even after the deformation force is removed.
Salt water taffy is a plastic material. Hence stretching of it will be a plastic deformation. Rubber-band is an elastic material.
Question 2
1 / -0

Linear elastic deformation is governed by ________

A
Hooke's Law

B
Euler Bernoulli's equation

C
both

D
none

Solution

$$Answer:-$$ A
Hooke's law- A law stating that the strain in a solid is proportional to the applied stress within the elastic limit of that solid.
In other words stress strain curve is linear before this yield point (see figure) and this is the region of elastic deformation and reversible.
Question 3
1 / -0

The Bulk Modulus for an incompressible liquid is?

A
zero

B
unity

C
infinity

D
between $$0$$ and $$1$$

Solution

Since liquid is incompressible there is no change in volume.
When strain is small the ratio of the normal stress to the volume strain is called the bulk modulus of material of the body.
$$B=\displaystyle\frac{normal stress}{volume strain}$$
$$=$$normal stress
change in volume$$/$$ original volume
since, the liquid is incompressible change in volume is zero.
$$B=\displaystyle\frac{normal stress}{o}=\infty$$
Hence, bulk modulus is infinite.
Question 4
1 / -0

As compared to concrete, steel has compressive strength:

A
$$25$$ times less

B
equal

C
$$25$$ times more

D
$$5$$ times more

Solution

Compressive strength is the capacity of a material or structure to withstand loads tending to reduce size, as opposed to tensile strength, which withstands loads tending to elongate.
Compressive strength is one of the most important engineering property of Concrete which designers are concerned of. However the compressive strength of steel is around 25 time more than that of concrete.
Question 5
1 / -0

Which of the following is not artificial form of plastics?

A
Nylon

B
Teflon

C
Styrofoam

D
None of the above

Solution

Plastic is a synthetic material made from a wide range of organic polymers such as polyethylene, PVC, nylon, etc., that can be moulded into shape while soft, and then set into a rigid or slightly elastic form.
Nylon, teflon and styrofoam are all examples of plastics.
Question 6
1 / -0

The ratio of hydraulic stress to the corresponding strain is known as

A
Compressibility

B
Bulk modulus

C
Young's modulus

D
Rigidity modulus

E
Expansion coefficient

Solution

Bulk modulus of elasticity is defined as ratio of hydraulic stress to the corresponding the volumetric strain within the elastic limit.
Bulk modulus $$K=\dfrac {FV}{A\Delta V}=\dfrac {\Delta p\cdot V}{\Delta V}$$
where, $$\Delta p = \frac {F}{A} = $$ change in pressure.
Question 7
1 / -0

The dimensions of strain is:

A
$$L$$

B
$$L^{2}$$

C
It is dimensionless

D
$$ML^{2}T^{-2}$$

Solution

Strain is a measure of deformation representing the displacement between particles in the body relative to a reference length.
Linear strain is given by:
$$e = \cfrac{\Delta L}{L}$$

Dimensions of strain are:
$$[e] = \cfrac{[M^0 L^1 T^0]}{[M^0L^1T^0]} = [M^0L^0T^0]$$

Hence, it is dimensionless.
Question 8
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The unit of stress is:

A
$$kg$$ $${m}^{-2}$$

B
$$N$$ $${kg}^{-1}$$

C
$$N{m}^{-2}$$

D
$$N$$

Solution

Stress is defined as force per unit area.
$$\therefore stress(P)-\cfrac{F}{A}$$
$$\therefore$$ its SI unit= $$N/{m}^{2}$$
Question 9
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A steel cable with a radius $$2cm$$ supports a chairlift at a ski area. If the maximum stress is not to exceed $${ 10 }^{ 8 }N\quad { m }^{ -2 }$$, the maximum load the cable can support is

A
$$4\pi \times { 10 }^{ 5 }N$$

B
$$4\pi \times { 10 }^{ 4 }N$$

C
$$2\pi \times { 10 }^{ 5 }N$$

D
$$2\pi \times { 10 }^{ 4 }N$$

Solution

Here $$r=2cm=2\times { 10 }^{ -2 }m$$
Maximum load$$=$$ Maximum stress $$\times$$ Area of cross section
$$={ 10 }^{ 8 }N\quad { m }^{ -2 }\times \pi \times { \left( 2\times { 10 }^{ -2 }\quad { m }^{ } \right) }^{ 2 }=4\pi { 10 }^{ 4 }N$$
Question 10
1 / -0

For a perfectly rigid body

A
Young's modulus is infinite and bulk modulus is zero

B
Young's modulus is zero and bulk modulus is infinite

C
Young's modulus is infinite and bulk modulus is also infinite

D
Young's modulus is zero and bulk modulus is also zero

Solution

Young's modulus for a rigid body,
$$Y=\dfrac{Stress}{Strain}$$
Since, the perfect rigid body won't yield any strain, irrespective of the amount of stress.
$$Y=\dfrac{stress}{0}=infinite$$
Bulk modulus for a rigid body is infinite because the rigid body is incompressible.
The correct option is C.

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Re-Attempt Weekly Quiz Competition

Mechanical Properties of Solids Test - 13

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Mechanical Properties of Solids Test - 13

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SHARING IS CARING

Question 1

stretching a rubber band

stretching salt water taffy

none

both

Solution

Question 2

Hooke's Law

Euler Bernoulli's equation

both

none

Solution

Question 3

zero

unity

infinity

between $$0$$ and $$1$$

Solution

Question 4

$$25$$ times less

equal

$$25$$ times more

$$5$$ times more

Solution

Question 5

Nylon

Teflon

Styrofoam

None of the above

Solution

Question 6

Compressibility

Bulk modulus

Young's modulus

Rigidity modulus

Expansion coefficient

Solution

Question 7

$$L$$

$$L^{2}$$

It is dimensionless

$$ML^{2}T^{-2}$$

Solution

Question 8

$$kg$$ $${m}^{-2}$$

$$N$$ $${kg}^{-1}$$

$$N{m}^{-2}$$

$$N$$

Solution

Question 9

$$4\pi \times { 10 }^{ 5 }N$$

$$4\pi \times { 10 }^{ 4 }N$$

$$2\pi \times { 10 }^{ 5 }N$$

$$2\pi \times { 10 }^{ 4 }N$$

Solution

Question 10

Young's modulus is infinite and bulk modulus is zero

Young's modulus is zero and bulk modulus is infinite

Young's modulus is infinite and bulk modulus is also infinite

Young's modulus is zero and bulk modulus is also zero

Solution

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