Q#14 (Past Exam Paper – November 2009 Paper 11 Q22 & Paper 12 Q21)
A steel string on an electric guitar has the following properties.
diameter = 5.0 × 10-4 m
Young modulus = 2.0 × 1011 Pa
tension = 20 N
The string snaps, and contracts elastically.
By what percentage does a length l of a piece of the string contract?
A 5.1×10-4 %
B 5.1×10-2 %
C 1.3×10-4 %
D 1.3×10-2 %
B 5.1×10-2 %
C 1.3×10-4 %
D 1.3×10-2 %
Solution:
Answer: B.
Percentage of the length that contracts = e/L × 100%
But e/L is the strain of the string.
So, percentage of the length that contracts = strain × 100%
Young modulus, E = stress / strain
Strain = Stress / E
Stress = F / A
Strain = F / EA
Cross-sectional area. A = πd2 / 4
Strain = 20 / [(2.0×1011) × (π×(5.0×10-4)2/4)]
Strain × 100% = {20 / [(2.0×1011) × (π×(5.0×10-4)2/4)]} × 100%
Strain × 100% = 0.0509 % = 5.1×10-2 %
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