# Searle’s Method for Determination of Young’s modulus

## Searle’s Method:

With the help of a screw gauge, the average diameter of the experimental wire is measured. The length (l) of the experimental wire can also be determined using a metre scale.

The load applied at the end of the wire is then gradually increased. Measuring the corresponding extensions with suitably fitted verniers, a graph can be plotted with the load along the x-axis and the elongation along the y-axis. The graph passes through the origin and is a straight line below the figure.

As the graph is a straight line, we can say that load ∝ elongation, i.e, stress ∝ strain (within the elastic limit). This proves the validity of Hooke’s law.

## Young’s modulus experiment by Searle’s method:

Calculation: Form any point P on the graph, two perpendiculars are drawn on the axes.

Here, OQ = load (mg); OR = elongation (l)
Therefore, the longitudinal stress = mg/πr2 and the longitudinal strain = l/L

∴ Y = longitudinal stress / longitudinal strain
= mg/πr2/l/L = mgL/πr2l

Since the quantities on the right-hand side of the above expression are known the value of Young’s modulus (Y) can be determined.