We are going to determine the modulus of elasticity for the material of a wire using Sir's apparatus. The property of a body to regain its original shape and size once the deforming force is removed is called elasticity. The modulus measures the extent of elasticity for any material. If the wire is made of a material, this elasticity modulus is called Young's modulus of elasticity. Sir's apparatus, it consists of two metal frames P and Q hinged together such that they can move relative to each other in vertical direction. A spirit level is supported on a rigid cross bar frame which rests on the tip of a micro meter at one end and on a knife edge on the other. Screw can move vertically. The frames are suspended by two identical long wire of the same material. Wire on the side of the screw is called experimental wire and the other is called the reference wire. The frames are provided with hooks at the lower end from which weights are suspended. This wire carries a constant weight to keep the wire straight and taut. Slotted weights can be placed to apply force to the experimental wire. Principle, it works on the principle of Hooke's law. If delta L is the extension in the wire of length L and radius R due to force F equal to M g, the Young's modulus of the material of the wire is Y is equal to M g into L divided by pi R square delta L. Let us analyze our observations. Our observations for the diameter of the experimental wire, you must take at least three readings at different locations and find the average or mean value. Our observation table looks like this. The first column has load on hanger in kilograms, micrometer reading loading in millimeters, micrometer reading unloading in millimeters, you have a column for mean or average value and you have the last column for extension for 2 kg load. Let us see how we can analyze the observation and calculate the value for Y. In the last column, we are going to put extension for 2 kilograms. How are we going to do that is by choosing say 2.5 and 0.5. So the reading for 2.5 minus that for 0.5 will give me the extension for 2 kilograms. This value comes out to be 1.11. Likewise with 3 and 1 kilogram, the difference will give me for 2 kilograms which will be 1.22. 3.5 minus the reading for micrometer for 1.5 kilograms. Again, will give me 2 kilogram and that will be 1.22. Average that out and your reading is 1.18 millimeters. You can put all the values in meters. This calculation in SI unit after plugging the values in the formula will be giving us m g l upon pi r square delta l and the result can be calculated as 7.31 into 10 is part of 10 Newton meter square. We can also find the value of Young's modulus using a graph. So if you plot a graph of load and extension, keeping the load on the x axis and extension on the y axis, you will get a straight line. Within experimental error, the slope of the line can be found accurately and this can be placed in the formula for y equal to l upon pi r square into 1 upon slope. Now, why should we have 2 wires? We load one and compare its extended length with the other unloaded wire. Why should the 2 wires be thin and long? So that small deforming force produces significant strain. Why should the 2 wires be of the same material? Because temperature can influence the material of the wire, the reference and the experimental wire are subjected to the same changes in condition and therefore, it is only the load which is responsible for its extension. Why should we measure the diameter of the wire at different positions to check its uniformity? Is the value for diameter going to change during the experiment? Yes it will because you are elongating the wire. Under the deforming force, its diameter is bound to become lesser. What the value of y change if we reduce the length of the wire? No, it would not. Why? It is the material property. However, you would get very small values of extension because the stress remains the same deforming force by unit area. The material has not changed so y will remain the same and in order to keep that constant, the value for strain will be very much smaller. So the extension would be difficult to measure. What is the role of spirit level in this experiment? And why do we have to keep leveling it? The leveling of spirit level at the beginning make sure that the reference wire and the experimental wire are of the same length. After adding or subtracting load, the experimental wire elongates or contracts. So you have to use the spirit level again and bring the bubble back to the center in order to check out the extension. Why should we adjust the spirit level only after sufficient time gap? When you load the experimental wire, it takes some time to extend completely and we have to allow for this time otherwise your reading would not be accurate. Now which of the quantities in all your measurements is going to have the largest effect on your calculation? It is easy to understand that it would be the diameter of the wire because you are taking r as a square and also the extension which is measured in millimeters by the micrometer. Now what is backlash error? And why should we keep it in mind? Backlash is play or loss motion between loosely fitting machine parts. The micrometer screw is loosely moving about its axis. While recording extension, the screw should be moved gently, slowly and only in one direction. The circular scale motion in a screw should match the linear motion to avoid backlash error. So, we have learnt today how to measure the modulus of elasticity using a wire which meant that we were looking only for Young's modulus of elasticity. You can do similar experiment by changing the material of the wire. You can choose copper wire though it is very very soft and your hanger assembly weight should change in order to not to cross the elastic limit. You can work it for stainless steel or steel wires, iron wires and a lot of other experiments can be done to determine Young's modulus of elasticity for wires which are commonly in use.