Relation Between Young's Modulus and Bulk Modulus

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Young's Modulus and Bulk Modulus are two important mechanical properties of solids along with the Shear Modulus.

Young’s Modulus is the ability of any material to resist the change in length for linear elastic solids such as rods and wires.
Bulk Modulus is the ability of any material to resist the change in volume.
Young’s Modulus is denoted by the symbol ‘Y’ or ‘E’ while Bulk Modulus is denoted by ‘K’ or ‘B’.

Relation Between Young's Modulus and Bulk Modulus is given as:

Where K is Bulk Modulus, Y is Young’s Modulus and µ is the Poisson’s Ratio.

Table of Content

What is Young’s Modulus?
What is Bulk Modulus?
Relation Between Young’s Modulus and Bulk Modulus
Relation Between Young’s Modulus and Bulk Modulus Derivation
Things to Remember
Previous Years’ Questions
Sample Questions

Key Terms: Young’s Modulus, Bulk Modulus, Longitudinal Stress, Volumetric Stress, Bulk Modulus Formula, Young’s Modulus Formula

What is Young’s Modulus?

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Young’s Modulus is defined as the mechanical property of a material to withstand compression or elongation with respect to its length.

It is the ratio of longitudinal stress to the longitudinal strain.
It is also referred to as the ‘Modulus of Elasticity’.
The SI unit of Young’s Modulus is Nm-2 or Pascal (Pa).
The dimensional formula of Young’s Modulus is [ML-1T-2].

Young’s Modulus

Young’s Modulus Formula is given as:

Y = Longitudinal StressLongitudinal Strain

Y = Ɛ

Where

Y is Young’s Modulus in Pa.
???? is Uniaxial Stress in Pa.
ε is Strain or Proportional Deformation.

Read More:

Relevant Concepts
Derivation Relation Between Elastic Constants	Stress and Strain Curve	Shearing Stress
Solid Deformation	Thermal Stress	Yield Strength
Dynamic Viscosity	Difference between Force and Pressure	Elastomers

What is Bulk Modulus?

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Bulk Modulus is defined as a measure of the resistance of a substance to uniform compression.

It is the ratio of volumetric or bulk stress to the volumetric or bulk strain.
It is also referred to as ‘Volume Strain Modulus’.
The SI unit of Bulk Modulus is Nm-2 or Pascal (Pa).
The dimensional formula of Bulk Modulus is [M1L-1T-2].

Bulk Modulus Formula is given as:

K = Volumetric/Bulk StressVolumetric/Bulk Strain

K = Δ PΔ V/V

Where

K is Bulk Modulus.
ΔP is the Change in the Pressure or Force Applied Per Unit Area.
V is the Initial Volume of the Material.
ΔV is the Change in the Volume of the Material due to the compression.

Bulk Modulus

Relation Between Young’s Modulus and Bulk Modulus

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Young’s Modulus and Bulk Modulus are two mechanical properties of solids. Young's Modulus is defined as the ability of any material to resist the change along its length while Bulk Modulus is the ability of any material to resist the change in its volume.

Relation between Young’s Modulus and Bulk Modulus is expressed as

Where

K denotes Bulk Modulus.
Y denotes Young’s Modulus.
μ denotes Poisson’s Ratio.

Relation Between Young’s Modulus and Bulk Modulus Derivation

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Young’s Modulus is defined as the ratio of longitudinal stress to longitudinal strain. It is denoted by Y and is mathematically given as:

Y = Longitudinal StressLongitudinal Strain

Y = Ɛ

On rearranging:

Ɛ =Y

When the deforming force is along the x direction, then,

Ɛx =Y - 1mY - 1mY

Here, the negative sign expresses the reduction in diameter when longitudinal stress is along the x-axis.

1/m arises because of the compression along the other two directions.

When the deforming force is along the y-direction, then,

Ɛy =Y - 1mY - 1mY

When the deforming force is along the z-direction, then,

Ɛz = Y - 1mY - 1mY

Volumetric Strain is given as

Ɛv = Ɛx + Ɛy + Ɛz

Substitute the corresponding values to Ɛx , Ɛy, Ɛz

Ɛv =3Y [1 - 2m]

Bulk Modulus is defined as the ratio of volumetric or bulk stress to volumetric or bulk strain. It is represented by K and is mathematically given as

K = Volumetric/Bulk StressVolumetric/Bulk Strain

K = Ɛv

Substituting

Ɛv = 3Y [1 - 2m]

In the above equation, it is obtained that

K =3σY [1 - 2m]

Thus, the mathematical relation between the Bulk Modulus (K) and Youngs Modulus (E) is given by:

K = Y3 [1 - 2m]

Check More:

Relevant Concepts
Surface Tension	Viscosity	Shear Modulus Formula
Torque	Tensile Stress	Stress and Strain
Stress Formula	Strain Energy	Elastic Limit

Things to Remember

Young’s Modulus is a measure of the ability of a material to withstand changes in length under compression.
Young’s Modulus is the ratio of longitudinal stress to longitudinal strain.
Bulk Modulus is defined as the change in the volume of a body produced when it undergoes compression on all sides.
Bulk Modulus is the ratio of volumetric stress to volumetric strain.
The S.I. unit for both Young’s Modulus and Bulk Modulus is Nm-2 or Pascal (Pa).
Relation Between Young's Modulus And Bulk Modulus is .

Previous Years’ Questions

Bulk modulus of water is 2×10 9 N/m2. The change in pressure… (Punjab PMET - 2011)
Young modulus of a perfectly rigid body is… (KCET - 2020)
The relation between Shear modulus (G), Young modulus… (J & K CET - 2019)
The bulk modulus of a perfectly rigid body is…
The bulk modulus of a fluid is inversely proportional to… (JIPMER - 1996)
Bulk modulus of elasticity (K) represents incompressibility…
How does the isothermal bulk modulus…
The relationship between Young's modulus Y, bulk modulus…
The dimension of the modulus of rigidity is… (AIIMS - 1994)
The ratio of shearing stress to the shearing strain is defined…

Sample Questions

Ques. What will be the bulk modulus of a liquid compressed in a cylinder from 0.0125 m3 volume at 80 N/cm2 pressure to 0.0124 m3 volume at 150 N/cm2 pressure? (3 Marks)

Ans. Given that

ΔP = 150 – 80 = 70 N/cm2
ΔV = 0.0124 – 0.0125 = -0.0001 m3
V = 0.0125 m3

Using the Bulk Modulus Formula,

K = ΔP × V / ΔV

K = 70 × 0.0125 / 0.0001

K = 8750 N/cm2

Therefore, the bulk modulus of the liquid is calculated as 8750 N/cm2.

Ques. What will be Young’s Modulus of a material whose elastic stress and strain are 4 N/m2 and 0.15, respectively? (3 Marks)

Ans. Given that

Stress, σ = 4 N/m2
Strain, ε = 0.15

Using Young’s Modulus Formula,

E = σ / ϵ

E = 4 / 0.15 =26.66 N/m22

Ques. What is Young’s Modulus? (3 Marks)

Ans. Young’s Modulus is defined as the ratio of longitudinal stress to the longitudinal strain. It is represented by Y. It describes the relationship between stress (force per unit area) and strain (proportional deformation in an object). It is measured in Pascals (Pa).

Young’s Modulus Formula is given as

Y = longitudinal stresslongitudinal strain

Y =Ɛ

Ques. What is Bulk Modulus? (3 Marks)

Ans. Bulk Modulus is defined as the ratio of volumetric or bulk stress to the volumetric or bulk strain. It is represented by K. It is defined as the change in the volume of a body produced when it undergoes compression on all sides.

Bulk Modulus Formula is given as

K = Volumetric/Bulk stressVolumetric/Bulk strain

K =Ɛv

Ques. What is the value of Young’s modulus for a perfectly rigid body? (1 Mark)

Ans. The value of Young’s modulus for a perfectly rigid body is infinite.

Ques. The change in pressure is 80 N/Cm2, and the actual volume of the object is 0.128 m3. What will be the volume change if the bulk modulus is 7390 N/cm2? (3 Marks)

Ans. Given that,

ΔP = 80 N/cm2
K = 7390 N/cm2
V = 0.128 m3

Using the Bulk Modulus Formula,

K = ΔP × V / ΔV

ΔV = ΔP × V / K

ΔV = 80 × 0.128 / 7390

ΔV = 10.24 / 7390

ΔV = 0.0013 m3

Ques. How does Young’s modulus change with a rise in temperature? (1 Mark)

Ans. Young’s modulus of a material decreases with a rise in temperature.

Ques. Why is a spring made of steel, not copper? (2 Marks)

Ans. A spring will be a better one if a large restoring force is set up in it on being deformed, which in turn depends upon the elasticity of the material of the spring. Since Young’s modulus of elasticity of steel is more than that of copper, hence steel is preferred in making springs.

Ques. Determine Young’s modulus of a material whose elastic stress and strain are 10 N/m2 and 0.15, respectively. (3 Marks)

Ans. Given that

σ = 10 N/m2
Strain, ε = 0.15

Using Young’s Modulus Formula,

Y =Ɛ

Y = 10 / 0.15

Y = 0.66 x 102 N/m2

Ques. What pressure should be applied to a lead block to reduce its volume by 20% if the Bulk Modulus is 5 × 1010 N/m²? (3 Marks)

Ans. Given that

Volumetric Strain = 20 % = 20 × 10-2
Bulk Modulus of Elasticity (K) = 5 × 1010 N/m²
Pressure Intensity or Volumetric Stress =?

Using Bulk Modulus Formula,

K = Volumetric stressVolumetric strain

Volumetric Stress = K x Volumetric Strain

Volumetric Stress = 5 × 1010 x 20 × 10-2 = 1010 N/m²

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Relation Between Young's Modulus and Bulk Modulus

What is Young’s Modulus?

Young’s Modulus Formula is given as:

What is Bulk Modulus?

Bulk Modulus Formula is given as:

Relation Between Young’s Modulus and Bulk Modulus

Relation Between Young’s Modulus and Bulk Modulus Derivation

Things to Remember

Previous Years’ Questions

Sample Questions

CBSE CLASS XII Related Questions

1.
Write two advantages of reflecting telescope over refracting telescope.

2.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

5.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

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Relation Between Young's Modulus and Bulk Modulus

What is Young’s Modulus?

Young’s Modulus Formula is given as:

What is Bulk Modulus?

Bulk Modulus Formula is given as:

Relation Between Young’s Modulus and Bulk Modulus

Relation Between Young’s Modulus and Bulk Modulus Derivation

Things to Remember

Previous Years’ Questions

Sample Questions

CBSE CLASS XII Related Questions

1.Write two advantages of reflecting telescope over refracting telescope.

2.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

5.Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Write two advantages of reflecting telescope over refracting telescope.

2.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

5.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?