Young's modulus - Uniform bending (Single optic lever 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 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 uniform bending technique.

Young's modulus - Uniform bending

(Single optic lever method)

Aim:

To determine the Young's modulus of the material of the given beam subjecting it to uniform bending using a single optic lever.

Apparatus required:

The given beam, knife edges, weight hangers with weights, a single optic lever, scale and telescope arrangement, Vernier caliper, screw gauge, etc.

Formula:

Young’s modulus,

 

Here,

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

m is the load kg

g is the acceleration due to gravity m/s2

a is the distance between the point of suspension of the load and the nearer knife-edge m

D is the distance between the single optic lever mirror and the scale in the telescope arrangement m

l is the perpendicular distance between front leg and the line joining the hind legs of the optic lever m

L is the distance between the two knife edges m

b is the breadth of the beam m

d is the thickness of the beam m

s is the shift in the scale reading m

Procedure:

        The rectangular beam is evenly supported on knife edges spaced a distance ‘L’ apart. Two weight hangers are suspended at a distance ‘a’ (say 10 cm) from ends of the bar. An optic lever's front leg is positioned at the center, while the back legs rest on a platform that matches the height of the knife edges.

A scale and telescope arrangement are set up about one meter away from the mirror of the optic lever. The horizontal cross-wire in the telescope is aligned with a specific division on the scale, and the reading is recorded.

Weights are then added to the two hangers in increments of ‘m’ (say, 50 gm), and the corresponding readings from the telescope are noted. This process is repeated while removing the weights as well, and all readings are organized into a table. From these measurements (m/s) can be calculated.

        This ratio can also be calculated by plotting a graph, with shifts in the scale reading ‘s’ 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/s).

The beam's width ‘b’ and thickness ‘d’, using a Vernier caliper and a screw gauge, respectively. The distance ‘D’ from the mirror of the optic lever to the vertical scale on the telescope is also measured. An impression of the three legs of the optic lever is created on a paper, and the perpendicular distance ‘l’ between the front leg and the line connecting the hind legs is measured.

Tabular Column 1: To find the shift (s) corresponding to the load (m)

Load ‘m’ gm	Telescope scale readings						Mean cm	Shift in the scale reading for 100 gm ‘s’ cm
	Loading cm			Unloading cm
w
w+50
w+100
w+150
w+200
w+250

Tabular Column 2: To find the breadth of the beam using Vernier calliper

            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 beam by the method of non uniform bending using single optic lever is found to be, E = _____ N/m2