Physics, asked by cparmar4789, 11 months ago

How youngs modulus and elevation at centre in uniform bending are related?

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Answered by sureshlita

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Young's Modulus Apparatus

Model: HO-ED-M-02Price : $ 1167.00Get Quote

Holmarc's Young's modulus apparatus (Model No: HO-ED-M-02) is used to measure the Young's modulus of a bar. Young's modulus is a measure of stiffness of an elastic material and is a quantity used to characterize materials. It can vary considerably depending on the exact composition of the material. If the beam is loaded at its mid-point, the depression produced will not form an arc of a circle. This type of bending is called non-uniform bending. If the beam is loaded at both ends, the elevation produced will form an arc of a circle. This type of bending is called uniform bending. Two methods are used to measure Young's modulus of the bar in both uniform and non-uniform bending. They are Pin and Microscope method and Optic lever method.

In non uniform bending, the beam (meter scale) is supported symmetrically on two knife edges and loaded at its centre. The maximum depression is produced at its centre. Since the load is applied only at a point of the beam, this bending is not uniform through out the beam and the bending of the beam is called non-uniform bending.

Non uniform bending

In uniform bending, the bar is placed symmetrically on two knife edges. Two weight hangers are suspended at equal distance from the knife edges. Weights are add one by one and corresponding readings are taken. From these readings, the mean elevation (e) of the midpoint of the bar for a given mass is determined.

Uniform bending

Experiment Examples

To find the Young's modulus of the material of a bar by uniform and non uniform bending using,

1. Pin and microscope method

2. Optic Lever Method

Schematic Diagram