Hookes law : With in the elastic limit, stress is directly proportional to the strain.
Stress ∝ strain; Stress = k × strain. Where k is modulus of elasticity.
Determination of young's modulus of the material of a wire :
1. It consists of two long straight wires of same length and same area of cross-section suspended side by side from a rigid support.
2. The wire A (reference wire) carries a metre scale M and a pan to place a weight.
3. The wire B (experimental wire) carries a pan in which known weights can be placed.
4. A vernier scale v is attached to a pointer at the bottom of the experimental wire B and the main scale M is fixed to the wire A.
5. The weights placed in the pan, the elongation of the wire is measured by the vernier arrangement.
6. The reference wire is used to compensate for any change in length that may occur due to change in room temperature.
7. Both the reference and experimental wires are given an initial small load to keep the wires straight and the vernier reading is noted.
8. Now the experimental wire is gradually loaded with more weights, the vernier reading is noted again.
9. The difference between two vernier readings gives the elongation produced in the wire.
10. Let r and L be the radius and initial length of the experimental wire. Let M be the mass that produced an elongation ∆L in the wire.
Young's modulus of the material of the experimental wire is given by
y = (longitudinal stress/ longitudinal strain)
y = FL/A∆L;
y = (MgL/πr2 x ∆L)
From above equation young's modulus of the material of the wire is determined.
