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## Aim

To find the Young's modulus of the given material bar by uniform bending using pin and microscope method.

## Apparatus

Pin and Microscope arrangement, Scale ,Vernier calipers, Screw gauge, Weight hanger, Material bar or rod.

## Theory

Young’s modulus is named after Thomas Young,19th century ,British scientist. In solid mechanics, Young’s modulus is defines as the ratio of the longitudinal stress over longitudinal strain, in the range of elasticity the Hook’s law holds (stress is directly proportional to strain). It is a measure of stiffness of elastic material.

If a wire of length L and area of cross-section 'a' be stretched by a force F and if a change (increase) of length 'l' is produced, then

## Uniform Bending Using Pin and Microscope Method

In uniform Bending , the Young’s modulus of the material of the bar is given by

(1)

Where,

m - Mass at each end of the bar.

p - Distance between the point of suspension of the mass and nearer knife edge.

g - Acceleration due to gravity.

*l * is the length of the bar between the knife edges.

e - Elevation of the midpoint of the bar for a mass m at each end.

I - Geometrical moment of inertia.

For a bar of rectangular cross section,

(2)

Where b is the breadth and d is the thickness of the bar.

Substituting (2) in equation (1)

** **(3)

From graph, can be calculated.

### ** **** **** **** **** ** Applications

1. Thin film applications.

2.It helps to predict the directional and orientation properties of metals and has application in ceramics.

3. Measurement of soft tissues -early detection, elasticity imaging, etc.

4. It is used to test equipments like ultrasonic transducers, ultrasonic sensors.