Page 92 - Physics - XI

Young's modulus: Within the elastic limit, the ratio of the normal stress to the longitudinal strain is called
Young's modulus. It is represented by the symbol Y. Let a wire of length L and area of cross-section A be
stretched by a force F, so that its length is increased by l, then

Normal stress = Force applied = F
Area of cross-section A

Longitudinal strain = Change in length = l
Original length L

Young's modulus = Normal stress = FA/
Longitudinal strain lL/
FL
Y =
Al
If extension is produced by suspending a long M from a wire of radius r then

F = Mg and A = πr 2

A Hence, Y = MgL
2
π r l

C D Procedure A
1. First of all, suspend the weights from the hooks in such a way that
the two wires are stretched and become free from any kinks. Attach
B a constant weight W on the hook A to keep the reference with taut. C D
Fig. 1.2: Diameter of the wire in two 2. Find the pitch and the least count of the screw gauge. Also, determine
mutually perpendicular directions
the zero correction for the screw gauge. With the help of the screw B
gauge, measure the diameter of the wire Y at six diff erent positions Fig. 1.2: Diameter of the wire
in two mutually perpendicular directions at every position as shown in two mutually
in Fig. 1.2. perpendicular directions
3. Measure the length of the wire Y with the help of the metre scale from the point of suspension T to the
2
point of attachment N′.
4. Find the breaking stress for the steel wire used and calculate the maximum load to be applied. Maximum
load should not exceed one third of the breaking stress.

Breaking load = Breaking stress × Area of cross-section.
5. Find the pitch and the least count of the micrometer attached to the apparatus. With no weights on the
hanger B, turn the micrometer screw gradually so that bubble of the spirit level stands exactly at the
centre. Note the micrometer reading.
6. Add a weight of half kilogram on the hanger and wait for a few minutes and adjust the micrometer
screw gradually till the bubble of the spirit level is exactly at the centre.
7. Go on increasing the load on the hanger H in steps of 0.5 kg and observe the reading on the micrometer
each time, after the bubble has been brought in the centre till a load of 3.5 kg is reached. During these
observations, the micrometer screw should move in upward direction only so that the backlash error
can be avoided.

8. Now, unload the wire by removing the weights in the same order (in the step of 0.5 kg) and take
the micrometer reading each time till all the weights on the hanger H are removed. During these

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