Hooke’s law MCQ Quiz - Objective Question with Answer for Hooke’s law - Download Free PDF

CONCEPT:

​Hooke's law

• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.

⇒ Stress ∝ Strain

⇒  Stress = E × Strain

Where E = modulus of elasticity

⇒  σ = Eϵ    

where σ = stress, ϵ = strain, and E = young's modulus of elasticity

EXPLANATION:

• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.
• So the Hooke's law defines the elastic limit. Hence, option 3 is correct.

\(Kx_0 + F_B = Mg\)

\(\displaystyle kx_0 + \sigma \frac{L}{2} AG =Mg\)

\(\displaystyle x_0 =\frac {Mg - \dfrac{\sigma LAg}{2}}{k} =\frac {Mg}{k} \left ( 1 -\frac {\sigma LA}{2M} \right )\)

Concept:

The young modulus is defined as the stress per unit strain i.e. \(Y=\frac{FL}{AΔ L}\) , where F is the force, L is the length , A is the cross sectional area Δ L is the change in length. It is the property of material. 

Explanation:

Let take the dx line element x distance from the origin. The young modulus will be

 \(Y=\frac{gxdm}{AΔ L} \\ Δ L= \frac{gxdm}{AY} \ \ \ \ \ \ \ \ \ \ (1)\)

And \(dm=\frac{mdx}{L}\)

Putting the dm in  (1).

\(Δ L= \frac{gm}{ALY}\int_0^Lxdx \\ Δ L= \frac{gmL}{2AY}\)

The correct option is (2).

CONCEPT:

• Hooke's Law: For small deformations, the stress is proportional to the strain produced. 

Stress ∝ strain

stress = k × strain

where k is the proportionality constant.

• Tensile stress:  The force applied along a rod divided by the cross-sectional area of the rod perpendicular to the applied force is called tensile stress.

\(\rm Tensile~stress = {Force \over Cross ~section ~area}\)

• Longitudinal strain: When there is a change in length either due to tensile stress or due to compressive stress, the strain produced is longitudinal strain.

\(Longitudinal ~strain = {Change~in~length~or~extension \over original ~length}= {Δ L \over L}\)

EXPLANATION:

Given that length = L and volume = V and Force = F 

Since in the stress formula we have to use area A that is not given in the question, So

Volume V = Area A × length L

A = V / L

From Hooke's law

stress = k × strain

\( {F \over A}=k \times {Δ L \over L}\)

\( {F \over V/L}=k \times {Δ L \over L} \)

\( {F L \over V}=k \times {Δ L \over L} \)

\( {F L^2 \over k V}= {Δ L } \)

So extension ΔL ∝ L²

• The extension produced in this wire by a constant force F is proportional to L².
• Hence the correct answer is option 4.

CONCEPT:

• Stress: Stress is the ratio of the load or force to the cross-sectional area of the material to which the load is applied.
  • The standard unit of stress is N/m².
• Strain: Strain is a measure of the deformation of the material as a result of the force applied.
  • The strain is a unitless quantity.
• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.

⇒ Strain ∝ Stress

⇒ Strain = E × Stress (Where E = modulus of elasticity)

• Hooke's law is important because it helps us understand how a stretchy object will behave when it is stretched or compacted.

• This law was named after Robert Hooke. 

EXPLANATION:

• According to Hook's law, stress ∝ strain. So option 1 is correct.

CONCEPT:

• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.

⇒ Strain ∝ Stress

⇒ Strain = E × Stress (Where E = modulus of elasticity)

• Hooke's law is important because it helps us understand how a stretchy object will behave when it is stretched or compacted.

EXPLANATION:

From the above explanation, we can see that according to Hooke’s law stress is directly proportional to strain:

i.e., \({\rm{Strain\;}} \propto {\rm{\;Stress}} \Rightarrow \frac{{stress}}{{strain}} = E\)

CONCEPT:

• Hooke's law states that " Within the elastic limit stress is directly proportional to strain"
• The stress of an elastic material is the restoring force acting per unit area of an object
• The strain is the ratio of change in dimension to the original dimension 

EXPLANATION:

• Hooke's law states that within the elastic limit stress is directly proportional to strain. Hence, option 1 is the answer
• The ratio of stress to strain is known as an elastic modulus. 

CONCEPT:

• Stress (σ): Stress is the ratio of the load or force to the cross-sectional area of the material to which the load is applied.
• The standard unit of stress is N/m2.
• ​Stress (σ) = Force (F)/Area (A)
• Strain (S): Strain is a measure of the deformation of the material as a result of the force applied.
• The strain is a unitless quantity.

Work done in deforming a body is given by:

\(\begin{array}{l} W = \frac{1}{2}σ S \\ W = \frac{1}{2} × stress × strain \end{array}\)

• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.

⇒ Stress ∝ Strain

⇒  Stress (σ) = Y × Strain (S)  (Where Y = modulus of elasticity)

CALCULATION:

Work done (W) = (1/2) × stress × strain = (1/2) × Y × S × S = \( \dfrac{1}{2}YS^2\)

So option 4 is correct.

CONCEPT:

• Elastomers: The substances that can be stretched to cause large strains are called elastomers.
  • Examples are the tissue of the aorta, rubber, etc.
• These materials do not obey Hooke’s law over most of the region.
• A typical stress-strain graph of an elastomer is given below:

Here we can clearly see that curve is not linear. To follow Hooke's law it is necessary that the curve should be in straight line.

EXPLANATION:

• Option 1: Plastic materials are the materials which when deformed does not return to their original state or show permanent deformation.
• Option 2: Elastic materials are the material which after deformation can regain their original shape and size.
• Option 3: The materials that can be stretched to cause large strains are called elastomers.
• So the correct answer is option 3.

CONCEPT:

• Stress: Stress is the ratio of the load or force to the cross-sectional area of the material to which the load is applied.
  • The standard unit of stress is N/m2.
• Strain: Strain is a measure of the deformation of the material as a result of the force applied.
  • The strain is a unitless quantity.
• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.

⇒ Strain ∝ Stress

⇒  Strain = E × Stress  (Where E = modulus of elasticity)

\( \Rightarrow σ=\frac{F(N)}{A(m^2)}\)    

\( \Rightarrow strain=\frac{dl}{l}\)    

\( \Rightarrow σ=strain\times E\)    

where σ = stress, F = applied force, A = cross-sectional area, dl = change in length, l = initial length and E = young's modulus of elasticity

EXPLANATION:

• The young's modulus of elasticity is a proportionality constant and it depends on the material.
• So modulus of elasticity does not depend on stress and strain.
• Hence, option 4 is correct.

CONCEPT:

• When we exert tensile stress on a wire, it will get stretched and work done in stretching the wire will be equal and opposite to the work done by inter-atomic restoring force. This work stored in the wire in the form of Elastic potential energy.
• Whereas work done can be derived as

\(⇒ W\; = \smallint F.dl\)

Where F = force applied on wire and dl = change in length

EXPLANATION:

• Now by using the relation of Young’s Modulus we can say that,

\(⇒ Y = \frac{F}{A} \times \frac{L}{{\rm{l}}} ⇒ F = \frac{{YAl}}{L}\)

Substituting the value of Y in the equation of work we get

\(⇒ W = \smallint \frac{{YAl}}{L}dl = \frac{{YA{l^2}}}{{2L}} = \frac{1}{2}\frac{YAl}{L}l\)

\(\Rightarrow W = \frac{1}{2}\times Force\times Elongation\)

CONCEPT:

​Hooke's law

• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.

⇒ Stress ∝ Strain

⇒  Stress = E × Strain

Where E = modulus of elasticity

⇒  σ = Eϵ    

where σ = stress, ϵ = strain, and E = young's modulus of elasticity

EXPLANATION:

• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.
• So the Hooke's law defines the elastic limit. Hence, option 3 is correct.

CONCEPT:

• Hooke's Law: For small deformations, the stress is proportional to the strain produced. 

Stress ∝ strain

stress = k × strain

where k is the proportionality constant. This constant is the property of the material and it is called Young's modulus of elasticity (γ).

EXPLANATION:

• According to Hooke's law, we know that

stress = k × strain

\(k = {stress \over strain}\)

• Here k is the ratio of stress and strain and this ratio is the property of the material and is constant.
• So if we increase the stress value, the ratio of stress and strain (proportionality constant k) will not change because it remains constant.
• Hence the correct answer is option 3.

CONCEPT:

• Stress: Stress is the ratio of the load or force to the cross-sectional area of the material to which the load is applied.
  • The standard unit of stress is N/m².
• Strain: Strain is a measure of the deformation of the material as a result of the force applied.
  • The strain is a unitless quantity.
• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced.

⇒ Strain ∝ Stress

⇒ Strain = E × Stress (Where E = modulus of elasticity)

• Hooke's law is important because it helps us understand how a stretchy object will behave when it is stretched or compacted.

• This law was named after Robert Hooke. 

EXPLANATION:

• According to Hook's law, stress ∝ strain. So option 1 is correct.

CONCEPT:

• Robert Hooke is best known to physicists for his discovery of the law of elasticity. 
  • This Hookes' law laid the basis for stress and strain study and understanding how the elastic materials behave.
• Ohm's law is known as the law of electricity. But there are also some other laws in the law of electricity.
• Gauss founded the law of flux.
• Newton founded the law of gravity.

EXPLANATION:

• Robert Hooke is best known to physicists for his discovery of the law of elasticity.
• So the correct answer is option 2.

• Some information about Robert Hooke:
  • He built a Gregorian reflecting telescope; discovered the fifth star in the trapezium and an asterism in the constellation Orion.
  • He suggested that Jupiter rotates on its axis; plotted detailed sketches of Mars which were later used in the 19th century to determine the planet’s rate of rotation
  • He stated the inverse square law to describe planetary motion, which Newton modified later etc. 
  • He built a Gregorian reflecting telescope.
  • He discovered the fifth star in the trapezium and an asterism in the constellation Orion.
  • He suggested that Jupiter rotates on its axis; plotted detailed sketches of Mars which were later used in the 19th century to determine the planet’s rate of rotation
  • He stated the inverse square law to describe planetary motion, which Newton modified later etc.