CBSE Physics Experiment Young’s Modulus of a Wire Using Searle’s Apparatus

With time, the perpetual need for the construction of more buildings, dams and bridges is increasing. For these industrial architects to become strong and durable, it is essential to have good knowledge of the modulus of elasticity of the material used for construction, i.e. the Young’s modulus, which we will study here.

Young’s modulus (Y) is defined as the ratio of tensile or compressive stress \[\sigma \] to the longitudinal strain \[\varepsilon \]:

\[Y = \dfrac{\sigma }{\varepsilon }\]

In this experiment, we are going to determine Young’s modulus Y of the material of a given wire using Searle’s apparatus, by determining the change in length of the wire under a constant weight using a screw gauge.

Table of Contents

• Aim

• Theory

• Procedure

• Observations

• Result

Aim

To determine Young’s modulus of the material of a given wire by Searle’s apparatus.

Apparatus required

• Searle apparatus

• Meter scale

• Small weights

• Given wire

• Screw gauge

• Spirit level

Theory

The arrangement consists of two frames that are allowed to move vertically relative to each other, joined by a spirit level. One of the frames holds a reference wire and the other one the experimental wire, which is connected to a screw gauge. Both the frames contain hooks for hanging weights to taut. Due to the additional weights, the experimental wire suffers a small length elongation, which disturbs the spirit level bubble. The screw gauge is used to adjust the bubble again at its middle position and hence gives the reading of the elongation.

The apparatus works on the principle of Hooke’s law. The Young’s modulus Y of the wire is given by:

\[Y = \dfrac{{MgL}}{{\pi {r^2}\Delta L}}\]

where M = Mass of the hanged weights

L = Original length of the wire

r = Radius of the wire

\[\Delta L\]= Extension in length of wire

g = Acceleration due to gravity

Procedure

1. Suspend small equal weights from both the wires to make them perfectly taut. Measure the length of each wire using a meter scale.

2. Determine the least count and zero error of the screw gauge. Determine the thickness of the given wire using a screw gauge at five different points on the wire. At each point, measure the thickness along two mutually perpendicular directions along its diameter and find the mean of the two. Divide it by 2 to get the radius.

3. Adjust the screw gauge such that the spirit level placed on the cross bar shows perfectly horizontal balance. Note the micrometer reading.

Searle’s Apparatus

4. Hang a weight of 0.5 kg to the given wire. The bubble in the spirit level will move away from the equilibrium position by a little bit. Adjust the screw gauge so as to bring it back to its equilibrium position. Note the reading in the screw gauge.

5. Increase the weight in steps of 0.5 kg and note the screw gauge reading in each case after using it to restore the position of the spirit level bubble.

6. Tabulate about 8 observations.

Observations

Length of the wire L = 

Least count (LC) of the screw gauge = 

Zero error of screw gauge = 

Observation Table – For the radius of wire

MSR = Main scale reading of screw gauge

CSD = Circular scale division coinciding of screw gauge

Mean diameter after correcting zero error = 

Mean radius = 

Observation Table – For the Extension of Wire

Observation Table – Mean Extension in Wire Per 2 kg Load

Therefore, \[mean\;\Delta L = \dfrac{{(e - a) + (f - b) + (g - c) + (h - d)}}{4}\;cm\; = \;............\;cm\] for 2 kg

Result

Young’s modulus of the material of wire,

\[Y = \dfrac{{MgL}}{{\pi {r^2}\Delta L}} = ...........\;N{m^{ - 2}}\]

Precautions

1. Both wires should be taut and uniform at all points.

2. Measure the thickness of wires very carefully at both orthogonal positions on the same point.

3. Determine the zero and backlash errors of the screw gauge very carefully.

Lab Manual Questions

1. State elastic limit of a material and Hooke’s law.

Ans: The maximum applied stress allowed on a material up to the limit so as not to cause permanent deformation in it is known as the elastic limit of that material. Within this limit, the strain developed inside the material is directly proportional to the stress applied on it. This law is known as Hooke’s law.

2. Explain Young’s modulus of a material.

Ans: Young’s modulus of a material is defined as the ratio of tensile or compressive stress applied to a material to the longitudinal strain produced in that material. Its SI unit is \[N{m^{ - 2}}\].

3. On what factors does the Young’s modulus of a material depend?

Ans: Young’s modulus of a material is given by the formula

\[Y = \dfrac{{MgL}}{{\pi {r^2}\Delta L}}\]

It depends on the length L of the material, weight Mg used for deformation, its cross-sectional area \[\pi {r^2}\] and the amount of length deformation \[\Delta L\]. The value of Young’s modulus is constant for a given material but depends on external parameters such as temperature and pressure.

4. What is the rigidity modulus of a material?

Ans: Modulus of rigidity is defined as the ratio of shearing stress applied on a material to the shearing strain produced in that material. It is also known as shear modulus.

Viva Questions

1. Why does an elongation in a metallic rod hinged at one end in this experiment?

Ans: When the load is applied on the wire, the wire stretches by a small amount due to it. This strains the wire and hence the wire elongates.

2. In Young’s modulus experiment, why do we use two wires?

Ans: In Young’s modulus experiment, we use one reference wire and an experimental wire. The reference wire measures the small but finite elongation in the experimental wire due to applied load using a screw gauge.

3. Is it possible to determine the rigidity modulus of gases?

Ans: No, it is not simply possible to determine the rigidity modulus of gases because one cannot apply shearing stress on them due to large inter-particle separation and cannot measure their shearing strain.

4. In the above experiment, how do stress and strain get produced in the material?

Ans: In the above experiment, the stress is applied to the experimental wire by virtue of slotted weights, and the strain is produced in it in response due to stress applied in the form of longitudinal elongation of the wire.

5. What is Young’s modulus of elasticity?

Ans: Young’s modulus of elasticity is defined as the ratio of tensile stress to the longitudinal strain of material.

6. Give Young’s modulus formula.

Ans: The Young’s modulus Y of a material is given by:

\[Y = \dfrac{{MgL}}{{\pi {r^2}\Delta L}}\]

where F = Force applied on the material

A = Cross sectional area of the material

\[\Delta L\]= Length extension in the material

L = Given length of the material

7. If an elastic material with Young’s modulus Y is subjected to stretching stress S, obtain the expression for elastic energy stored per unit volume in the material.

Ans: Energy stored per unit volume = \[\dfrac{1}{2} \times Stress \times Strain\]

Since Young’s modulus \[Y = \dfrac{{Stress}}{{Strain}} = \dfrac{S}{{Strain}}\;\;\;\;\; \to \;\;\;\;\;Strain = \dfrac{S}{Y}\]

Therefore, energy stored per unit volume = \[\dfrac{1}{2} \times S \times \dfrac{S}{Y} = \dfrac{{{S^2}}}{{2Y}}\]

8. Define elastic deformation.

Ans: The deformation caused on an elastic body due to external deforming force before the body regains its initial shape and size is known as elastic deformation.

9. What is the shear modulus?

Ans: The ratio of shearing stress to the corresponding shearing strain of a material is known as the shear modulus of that material.

10.  Give three useful examples of elasticity in Physics.

Ans: Useful examples of elasticity in physics include rubber bands, springs and trampoline.

Practical Questions

1. What is the modulus of rigidity of ideal liquids?

1. Zero

2. Unity

3. 100

4. Infinite

Ans: (A) Zero

Since modulus of rigidity is a measure of rigidity of the body and ideal liquids are incompressible, non-viscous and have infinite shear strain, therefore the modulus of rigidity of ideal liquids is zero.

2. Choose the incorrect statement among the following:

1. Modulus of elasticity is a direct measure of the elasticity of the material

2. Elasticity of a material is inversely proportional to temperature

3. Modulus of rigidity of a material is directly proportional to temperature

4. For ideal fluids, bulk modulus is infinite

Ans: (C) 

Modulus of rigidity of a material is independent of temperature.

3. Hooke’s law specifies:

1. Stress

2. Strain

3. Modulus of elasticity

4. Elastic limit

Ans: (C) Hooke’s law specifies the modulus of elasticity as the ratio of stress to strain within the elastic limit.

4. On which factor does the breaking stress of a wire depend?

1. Material of wire

2. Length of wire

3. Thickness of wire

4. Shape of cross-section of wire

Ans: (A) The breaking stress of a wire depends upon the material of the wire.

5. The stress at which an elastic material transforms into a plastic material is known as:

1. Normal stress

2. Ultimate stress

3. Thermal stress

4. Yield strength

Ans: (D) The stress at which an elastic material transforms into a plastic material is known as yield strength.

6. How do the elastic properties of gold change when it is electroplated with another metal?

1. Decrease

2. Vanish

3. Increase

4. Remain unaffected

Ans: (C) When gold is being electroplated with another metal, its elastic properties increase due to an increase in impurity concentration.

7. How does hammering affect the elasticity of materials?

1. Has no effect

2. Elasticity increases

3. Elasticity decreases

4. Material loses its elasticity

Ans: (B) Hammering breaks down the material into smaller units that resist the deformation more effectively. Hence, elasticity increases.

8. Why does a bridge collapse when it experiences a heavy load?

1. Due to weak structure

2. Due to increase in stress

3. Due to faulty materials for construction

4. Due to friction

Ans: (A) Due to increase in stress (force per unit area)

9. What is the effect of annealing on elasticity?

1. Elasticity decreases

2. Elasticity remains same

3. Elasticity increases

4. Elasticity increases in some regions and decreases in others

Ans: (A) Annealing results in forming larger material crystals which resist deformation less effectively. Hence, elasticity decreases.

10. What should be done to prevent the breaking of rope under a large force?

1. Length should be increased

2. Small force should be applied

3. Rope’s cross sectional area should be increased

4. Rope made of a different material should be used

Ans: (C) Upon increasing the cross sectional area of the rope, the stress experienced by it decreases due to inverse proportionality.

Conclusion

From this experiment, we can conclude that elasticity plays a crucial role in physics and engineering. Good knowledge of the elasticity of various materials plays a very important role in the construction of houses, buildings, dams and much more. It also plays a significant role in our daily lives in the form of rubber bands, trampolines, springs etc.

We hope that the reader has got a good insight into the topic through this experiment and is encouraged to explore the relevant topics in Physics.