Mechanical Properties of Solids Test

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Mechanical Properties of Solids Test - 17

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Question 1
1 / -0

Consider the following two statements A and B and identify the correct answer.
A) When the length of a wire is doubled, the Young's modulus of the wire is also doubled
B) For elastic bodies Poisson's ratio is + Ve and for inelastic bodies Poissons ratio is -Ve

A
Both A & B are true

B
A is true but B is false

C
A is true but B is true

D
Both A & B are false

Solution

1/ Young's modulis is property of a metal independent of its dimensions
2/Definition of Poisson's ratio
Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio.Virtually all common materials, such as the blue rubber band on the right, become narrower in cross section when they are stretched.
Question 2
1 / -0

The poisson's ratio cannot have the value

A
0.7

B
0.2

C
0.1

D
0.3

Solution

The Poisson's ratio of a stable, isotropic, linear elastic material will be greater than −1.0 or less than 0.5 because of the requirement for Young's modulus, the shear modulus and bulk modulus to have positive values. Most materials have Poisson's ratio values ranging between 0.0 and 0.5.
Question 3
1 / -0

Consider the following two statements A and B and identify the correct answer.
A) The bulk modulus for an incompressible liquid is infinite.
B) Young's modulus increases with raise of temperature.

A
Both A & B are true

B
A is true but B is false

C
Both A & B are false

D
A is false but B is true

Solution

For an incompressible fluid volume change is zero. So as in expression of bulk modulus change in volume comes in denominator so the value of bulk modulus for incompressible fluid is infinity. Young's modulus decreases with increase in temperature.
Question 4
1 / -0

Consider the following two statements A and B and identify the correct answer.
A) We cannot define Young's modulus and rigidity modulus for liquids and gases.
B) The theoretical limits of Poisson's ratio are 1 to 0.5

A
Both A & B are true

B
A is false but B is true

C
Both A & B are false

D
A is true but B is false

Solution

The reciprocal of the bulk modulus is called the compressibility of the substance. The amount of compression of solids and liquids is seen to be very small.Thus youngs modulus is not defined for liquids and gases
and Theoretical limits of = 1 to 0.5.
Question 5
1 / -0

Consider the statements A and B, identify the correct answer given below :
(A) : If the volume of a body remains unchanged when subjected to tensile strain, the value of poisson's ratio is 1/2.
(B) : Phosper bronze has low Young's modulus and high rigidity modulus.

A
A and B are correct

B
A and B are wrong

C
A is correct and B is wrong

D
A is wrong and B is right

Solution

Experimental value of poisson's ratio is always between $$0$$ to $$1/2$$ .
As Phosper bronze is solid so, value of young's modulus is also high.
Question 6
1 / -0

Strain energy per unit volume in a stretched string is

A
1/2 $$\times$$ Stress $$\times$$ Strain

B
Stress x Strain

C
(Stress x Strain)$$^{2}$$

D
Stress / Strain

Solution

strain energy$$=\dfrac{1}{2}\times stress\times strain$$
Work done by a force on a wire
W $$=\dfrac{Ay(\Delta L)^{2}}{2L}$$
$$=\dfrac{1}{2}(\dfrac{yA}{}\dfrac{\Delta L}{L})\Delta L$$
$$=\dfrac{1}{2}(y\dfrac{\Delta L}{L})(\dfrac{\Delta L}{L})(AL)$$
$$=\dfrac{1}{2}(stress)(strain)(volume)$$
(Work)/(volume)$$ =\dfrac{1}{2}(stress)(strain)$$
Option A
Question 7
1 / -0

Possible value of Poisson's ratio is

A
1

B
0.9

C
0.8

D
0.4

Solution

The Poisson's ratio of a stable, isotropic, linear elastic material cannot be less than $$1.0$$ nor greater than $$0.5$$. So only possible value among the options is $$0.4.$$
Question 8
1 / -0

Assertion (A) : Lead is more elastic than rubber.
Reason (R) : If the same load is attached to lead and rubber wires of the same cross-sectional area, the strain of lead is very much less than that of rubber.

A
Both assertion and reason are true and the reason is correct explanation of the assertion

B
Both assertion and reason are true, but reason is not correct explanation of the assertion

C
Assertion is true, but the reason is false

D
Assertion is false, but the reason is true

Solution

More elastic the material higher the Young's Modulus.
Young's Modulus of rubber is 0.01-0.1 Gpa whereas for Lead it is 16 Gpa.

Also, $$Y = (F/A)/l/L$$

F - Applied Force
A - Cross Section Area
l - Elongation/Decrease in Length
L - Actual Length
Therefore $$l/L = F/AY$$
for F,A same
$$l/L$$ is inversely proportional to $$Y$$
So, higher the Young's Modulus, lesser is the strain.
Question 9
1 / -0

Consider the following two statements A and B and identify the correct answer .
A) A metal wire held vertically is longer than when it placed on a horizontal table.
B) Due to its own weight, some elongation is produced when it is held vertically.

A
Both A & B are true

B
A is false but B is true

C
A is true but B is false

D
Both A & B are false

Solution

When metal wire is held vertically then due to gravity (it's own weight) a froce acts in downward direction which makes the wire slightly longer. On the other hand when wire is kept horizontally then it might appear slightly thick but not longer.
Question 10
1 / -0

The Poisson's ratio $$\sigma$$ should satisfy the relation :

A
-1< $$\sigma $$ < 0.5

B
-0.5 < $$\sigma $$ < 1.0

C
0.5 < $$\sigma $$ < 1.0

D
-1.0 < $$\sigma $$ < -0.5

Solution

Poisson's ratio is the ratio of transverse contradiction strain to longitudinal extension strain in the direction of stretching force.
The Poisson's ratio $$\sigma$$ should satisfy the relation,
$$-1<\sigma <0.5$$

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Re-Attempt Weekly Quiz Competition

Mechanical Properties of Solids Test - 17

Result

Mechanical Properties of Solids Test - 17

Score

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Rank

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SHARING IS CARING

Question 1

Both A & B are true

A is true but B is false

A is true but B is true

Both A & B are false

Solution

Question 2

0.7

0.2

0.1

0.3

Solution

Question 3

Both A & B are true

A is true but B is false

Both A & B are false

A is false but B is true

Solution

Question 4

Both A & B are true

A is false but B is true

Both A & B are false

A is true but B is false

Solution

Question 5

A and B are correct

A and B are wrong

A is correct and B is wrong

A is wrong and B is right

Solution

Question 6

1/2 $$\times$$ Stress $$\times$$ Strain

Stress x Strain

(Stress x Strain)$$^{2}$$

Stress / Strain

Solution

Question 7

1

0.9

0.8

0.4

Solution

Question 8

Both assertion and reason are true and the reason is correct explanation of the assertion

Both assertion and reason are true, but reason is not correct explanation of the assertion

Assertion is true, but the reason is false

Assertion is false, but the reason is true

Solution

Question 9

Both A & B are true

A is false but B is true

A is true but B is false

Both A & B are false

Solution

Question 10

-1< $$\sigma $$ < 0.5

-0.5 < $$\sigma $$ < 1.0

0.5 < $$\sigma $$ < 1.0

-1.0 < $$\sigma $$ < -0.5

Solution

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