in the searler's metod to determine the young's modulus of a wire , a steel wire of length 156cm and diameter 0.054cm is taken as experimental wire. the average increase in length for 1 1/2 kg wt is found to be o.o5o cm.Then young's modulus of the wire?
ANS:
1.)2.002* 10^11 N/m
To find the Young's modulus of the wire using Searle's method, we need to use the formula:
Young's modulus (Y) = (4 * M * g * L) / (π * d^2 * ΔL)
Where:
- M is the mass added to the wire (in kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- L is the original length of the wire (in m)
- d is the diameter of the wire (in m)
- ΔL is the average increase in length (in m)
Given information:
- M = 1 1/2 kg = 1.5 kg
- g = 9.8 m/s^2
- L = 156 cm = 1.56 m
- d = 0.054 cm = 0.00054 m
- ΔL = 0.050 cm = 0.00050 m
Substituting these values into the formula:
Young's modulus (Y) = (4 * 1.5 kg * 9.8 m/s^2 * 1.56 m) / (π * (0.00054 m)^2 * 0.00050 m)
Simplifying:
Young's modulus (Y) = (58.24 kg * m^2/s^2) / (3.1452 * 0.0002916 m^3)
Young's modulus (Y) ≈ 200.202 * 10^9 N/m^2
Rounding to appropriate precision, the Young's modulus of the wire is approximately 2.002 * 10^11 N/m^2.