Young's Modulus

# Our Objective

Our aim is to determine the Young’s modulus of elasticity of the material of a given wire using Searle’s apparatus.

# The Theory

## Before we move ahead, do you know what a Searle’s apparatus is?

Searle’s apparatus consists of two metal frames F1 and F2. Each frame has a torsion head at the upper side and a hook at the lower side. These frames are suspended from two wires AB and CD of same material, length and cross-section. The upper ends of the wires are screwed tightly in two torsion heads fixed in the same rigid support. A spirit level rests horizontally with  one end hinged in the frame F2. The other end of the spirit level rests on the tip of a spherometer screw, fitted in the frame F1. The spherometer screw can be rotated up and down along a vertical pitch scale marked in millimeters. The two frames are kept together by cross bars E1 and E2.

## Do you know Searle’s apparatus works on the principle of Hooke’s law?

Hooke’s law can be expressed in terms of stress and strain. Stress is the force on a unit area within a material that develops as a result of the externally applied force. Strain is the relative deformation produced by stress.

## Define Hooke’s Law

Hooke’s Law states that within the limit of elasticity, stress applied is directly proportional to strain produced. That is, the extension produced in a wire is directly proportional to the load attached to it.

If a wire of length L and radius r be loaded by a weight Mg and if l is the extension produced,

Then, normal stress =---------------(1)

And Longitudinal strain=-----------------(2)

## Hence, Young’s modulus

Y=

Where,
L – Length of the wire
l- Extension for a load M