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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

YoungÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s modulus is named after Thomas Young,19th century ,British scientist. In solid mechanics, YoungÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s modulus is defines as the ratio of the longitudinal stress over longitudinal strain, in the range of elasticity the HookÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢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 YoungÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢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.