Description
Young modulus Apparatus in Lahore
Searle’s apparatus is used for the measurement of Young’s modulus. It consists of two equallength wires that are attached to a rigid support. To understand how Searle’s apparatus is used to determine Young’s modulus of elasticity of the material of a given wire, read the experiment below.
Aim
To determine Young’s modulus of elasticity of the material of a given wire.
Materials Required
 Searle’s apparatus
 Two long steel wires of the same length and diameter
 A metre scale
 A screw gauge
 Eight 0.5 kg slotted weights
 1 kg hanger
Theory
The normal stress for a wire with length L and radius r is loaded with weight Mg where l is the increase in length, then normal stress is given as:
Y can be calculated as the values of L and r are known and l is found by the known Mg value.
Diagram
Observations
Length of experimental wire AB, L = ….. cm = ……m
Measurement of diameter of the wire
Pitch of the screw gauge (p) = 0.1 cm
No.of divisions on the circular scale = 100
Least count of screw gauge (L.C) = 0.1/100 = 0.001 cm
Zero error of screw gauge (e) = …….cm
Zero error of screw gauge (e) = e = ……cm
Diameter of experimental wire
Sl.no  Linear scale reading N (cm)  Circular scale reading  Total reading N+n×(LC)d
(cm) 

No.of divisions on reference line (n)  Value n×(LC)(cm)  
1.  d_{1}=  
d_{2}=  
2.  d_{3}=  
d_{4}=  
3.  d_{5}=  
d_{6}=  
4.  d_{7}=  
d_{8}=  
5.  d_{9}=  
d_{10}= 
Measurement for extension of the wire
Breaking stress for steel (from a table), B = ….. Nm^{2}
Area of a crosssection of a wire, πr^{2} = ….. cm^{2} = …….m^{2}
Breaking load = Bπr^{2} = …. N
(∵1 kg = 9.8 N)
1/3rd of breaking load = ….kg
Pitch of spherometer screw, (p) = 0.1 cm
No.of divisions in the disc = 100
Least count of spherometer (LC) = 0.1/100 = 0.001 cm
Load and extension
Sl.no  Load on hanger M (kg)  Spherometer screw reading  Extension for load 2.5 kg l(cm)  
Load increasing x(cm)  Load decreasing y (cm)  Mean z = (x+y)/2 (cm)  
1.  0.0  z_{1}=  
2.  0.5  z_{2}=  
3.  1.0  z_{3}=  
4.  1.5  z_{4}=  
5.  2.0  z_{5}=  
6.  2.5  z_{6}=  l_{1}=(z_{6}z_{1})=  
7.  3.0  z_{7}=  l_{2}=(z_{7}z_{2})=  
8.  3.5  z_{8}=  l_{3}=(z_{8}z_{3})=  
9.  4.0  z_{9}=  l_{4}=(z_{9}z_{4})= 
Calculations
From table 1
Mean observed diameter of the wire,
Mean corrected diameter of the wire,
d = (d_{0} + c) = ……cm = ……m
Mean radius of wire,
r = d/2 = ……m
From table 2
Mean extension for 2.5 kg load,
From formula,
Result
 The Young’s modulus for steel as determined by Searle’s apparatus = …….. Nm^{2}
 Straightline graph between load and extension shows that stress ∝ strain. This verifies Hooke’s law.
Percentage error
Actual value of Y for steel =…… Nm^{2}
The difference in values =……… Nm^{2}
Percentage error = (difference in values)/(actual value) = …….%
It is within the limits of experimental error.
Precautions
 The material, length, and crosssectional area of both the wires must be the same.
 The same rigid support should be used as a support for both the wires.
 Before starting the experiment, kinks should be removed.
 At different places, the diameter of the wire should be measured.
 Adding and removing the slotted weight should be done gently.
 After every addition or removal of weight, wait for two minutes.
 Increasing or decreasing weights should be done in regular steps.
Sources of Error
 The slotted weights might not be of standard weight.
 The wire used in the experiment may not be of uniform crosssectional area.
Viva Questions
Q1. State Hooke’s law.
Ans: Hooke’s law states that when the material has a load within the elastic limit, then the stress is directly proportional to the strain.
Q2. What is Poisson’s ratio?
Ans: Poisson’s ratio is defined as the ratio of lateral strain to longitudinal strain and is denoted by μ.
Q3. What is the yield point?
Ans: Yield point is defined as the stress beyond which the material becomes plastic.
Q4. What is the elastic limit?
Ans: Elastic limit is defined as the maximum limit to which a solid can be stretched without any permanent alteration of shape or size.
Reviews
There are no reviews yet.