Young's modulus - Non - uniform Bending (Pin and Microscope method)

    The TANSCHE curriculum for first year B.Sc. Physics practical emphasizes experiments that enhance theoretical knowledge through practical experience. A key experiment in this curriculum is measuring Young's Modulus through non-uniform bending with a pin and microscope. This experiment allows students to assess the elasticity of a material by observing how a beam bends evenly when a load is applied.

    In this blog post, we will provide a step-by-step guide to help you carry out the experiment correctly. From setting up the equipment to interpreting the results, this guide offers a thorough approach for students to accurately determine the Young’s modulus of a material using the non-uniform bending technique.

Young's modulus - Non uniform Bending

(Pin and Microscope method)

Aim:

To determine the Young's modulus of the material of a given bar by the method of non-uniform bending using a pin and microscope.

Apparatus required:

Uniform bar, wait hanger, weights, knife edges vernier microscope, screw gauge, vernier caliper etc

Formula:

Young’s modulus, 

      

Here,

E is the Young's modulus of the material of the bar N/m2

m is the load added in the weight hanger kg

g is the acceleration due to gravity m/s2

L is the length of the bar between the knife edges m

b is the breadth of the bar m

d is the thickness of the bar m

y is the depression of the midpoint of the bar due to a load ‘m’  m

Procedure:

The given bar is placed symmetrically on two knife edges separated by ‘L’ length  (say 60 cm). A weight hanger is suspended at the centre of the bar. A pin is fixed vertically at the centre of the bar using wax.

        The tip of the pin is made to coincide with the crosswire in the microscope. The initial reading of the microscope on its vertical scale is noted.

        Load weight ‘m’ (50 gm) on the weight hanger. Adjust the microscope so that the inverted image of the pin tip is again aligned with the horizontal crosswire and record the microscope readings. Then, add weights in m (50 gm) increments until the maximum load is reached. Eachtime, take the microscope readings. The weights are then removed in equal steps and the microscope readings are recorded each time. The average value of load is obtained. From these readings, the average elevation of the midpoint of the bar due to the load ‘m’ applied is determined. From these measurements (m/y) can be calculated.

This ratio can also be calculated by plotting a graph, with depression ‘y’ along the x-axis and the mass ‘m’ along the y-axis. This leads to a straight line. The slope of this line will give (m/y).

The breadth (b) and the thickness (d) of the bar are measured with the help of vernier caliper and screw gauge respectively. The experiment can be repeated with different values of L.

Tabular Column 1: To find the elevation corresponding to load using vernier microscope

Least count (LC) = 0.001 cm

Load ‘m’ gm	Microscope readings						Mean cm	Depression corresponding to 100 gm ‘y’ cm
	Loading			Unloading
	MSR cm	VSR cm	TR cm	MSR cm	VSR cm	TR   cm
w
w+50
w+100
w+150
w+200
w+250

Tabular Column 2: To find the breadth of the beam using vernier caliper

The procedure of using Vernier caliper and its table can be found here.

Tabular Column 3: To find the thickness of the beam using screw gauge

The procedure of using Screw gauge and its table can be found here.

Result: 

The Young’s modulus of the material of the given beam = _________ N/m2

You can simulate this experiment here Virtual lab.