Elasticity Test

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Elasticity Test - 5

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Weekly Quiz Competition

Question 1
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The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of the water. The water pressure at the bottom of the trench is about 1.1 × 10⁸ Pa. A steel ball of initial volume 0.32 m³ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom?

[Given : B_steel = 1.6 × 10¹¹ N m^-2]

A
1.01 × 10⁻³m³

B
2.2 × 10⁻⁴m³

C
1.9 × 10⁻³m³

D
None of these.

Solution

Hint: Apply the concept of Bulk modulus.

The pressure at the bottom, P=1.1 × 10⁸ Pa

Initial volume of steel ball = V = 0.32 m³

The bulk modulus of steel, B = 1.6×10¹¹ N m⁻²

Step 1: Use the formula of the bulk modulus.
Question 2
1 / -0

Select the correct alternative(s).

A
Elastic forces are not always conservative

B
Elastic forces are always conservative

C
Elastic forces are conservative only when Hooke's law is obeyed

D
Elastic forces are not conservative

Solution

Work done by elastic forces in a circular loop is not zero always so elastic forces are not always conservative.
Question 3
1 / -0

Which of the following affects the elasticity of a substance?

A
Change in temperature

B
Impurity in substance

C
Hammering

D
All of these

Solution

Change in temperature, impurity in substance, hammering affects the elasticity of substance.
Question 4
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Select the wrong definition.

A
Deforming Force - force that changes configuration of body

B
Elasticity - property of regaining original configuration

C
Plastic body - which can be easily melted

D
Elastic limit - beyond which material begins to flow

Solution

Plastics are materials that can be shaped and molded easily. Plastics become easier to mold and shape when they're hot, and they melt when they get enough.
Question 5
1 / -0

A uniform cubical block is subjected to volumetric compression, which decreases its each side by 2%. The Bulk strain produced in it is

A
0.03

B
0.02

C
0.06

D
0.12

Solution
Question 6
1 / -0

Due to the addition of impurities, the modulus of elasticity:

A
Decreases

B
Increases

C
Remains constant

D
May increase or decrease

Solution

Addition of impurities effects the elasticity as follows. If impurities added is more elastic then the material becomes more elastic and vice-versa
Question 7
1 / -0

A load of 2 kg produces an extension of 1 mm in a wire of 3 m in length and 1 mm in diameter. The Young's Modulus of wire will be

A
3.25 × 10¹⁰ Nm^-2

B
7.48×10¹² Nm²

C
7.48×10¹⁰Nm⁻²

D
7.48×10⁻¹⁰ Nm⁻²

Solution

The applied force (load) = F = mg

= 2×9.8 = 19.6 N

diameter = 1mm = 1×10⁻³ m

⇒ radius = d/2 = 0.5 × 10⁻³ m

Area = 3.14×0.25×10⁻⁶ m²

= 0.785×10⁻⁶
Question 8
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The value of Young's Modulus for a perfectly rigid body is

A
1

B
Less than 1

C
Zero

D
Infinite

Solution

Since for perfectly rigid body. Strain produced will be zero.

Young's modulus is given by
Question 9
1 / -0

A spherical ball contracts in a volume by 0.01% when subjected to a normal uniform pressure of 100 atm. The Bulk modulus of its material is

A
1.01×10¹¹ Nm²

B
1.01×10¹² Nm⁻²

C
1.01×10¹⁰ Nm⁻²

D
1.01×10¹³ Nm⁻²

Solution

Since the spherical contracts by 0.01%
Question 10
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A metallic rod of length l and cross-sectional area A is made of a material of Young's Modulus Y. If the rod is elongated by an amout y, then the work done is proportional to

A
y

B
1/y

C
y²

D
1/y²

Solution

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Elasticity Test - 5

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Question 1

1.01 × 10−3 m3

2.2 × 10−4 m3

1.9 × 10−3 m3

None of these.

Solution

Question 2

Elastic forces are not always conservative

Elastic forces are always conservative

Elastic forces are conservative only when Hooke's law is obeyed

Elastic forces are not conservative

Solution

Question 3

Change in temperature

Impurity in substance

Hammering

All of these

Solution

Question 4

Deforming Force - force that changes configuration of body

Elasticity - property of regaining original configuration

Plastic body - which can be easily melted

Elastic limit - beyond which material begins to flow

Solution

Question 5

0.03

0.02

0.06

0.12

Solution

Question 6

Decreases

Increases

Remains constant

May increase or decrease

Solution

Question 7

3.25 × 1010 Nm-2

7.48×1012 Nm2

7.48×1010 Nm−2

7.48×10−10 Nm−2

Solution

Question 8

1

Less than 1

Zero

Infinite

Solution

Question 9

1.01×1011 Nm2

1.01×1012 Nm−2

1.01×1010 Nm−2

1.01×1013 Nm−2

Solution

Question 10

y

1/y

y2

1/y2

Solution

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1.01 × 10⁻³m³

2.2 × 10⁻⁴m³

1.9 × 10⁻³m³

3.25 × 10¹⁰ Nm^-2

7.48×10¹² Nm²

7.48×10¹⁰Nm⁻²

7.48×10⁻¹⁰ Nm⁻²

1.01×10¹¹ Nm²

1.01×10¹² Nm⁻²

1.01×10¹⁰ Nm⁻²

1.01×10¹³ Nm⁻²

y²

1/y²