In an experiment to measure the Young modulus of a metal, a wire of the metal of diameter 0.25 mm

Q#5 (Past Exam Paper – November 2018 Paper 13 Q19)

In an experiment to measure the Young modulus of a metal, a wire of the metal of diameter 0.25 mm is clamped, as shown.



The wire passes from a clamp, around a frictionless pulley, and then to a second frictionless pulley where loads are applied to it. A marker is attached to the wire so that the total length of wire between the clamp and the marker is initially 3.70 m. A scale is fixed near to this marker.

The graph shows how the reading on the scale varies with F.


What is the Young modulus of the metal?
5.5 × 1010 Pa           
9.4 × 1010 Pa           
1.6 × 1011 Pa           
2.2 × 1011 Pa



Solution:
Answer: D.


Young modulus E = stress / strain

Stress = Force / Area = F / A

Strain = extension / original length = e / L


E = (F/A) / (e/L) = FL / Ae


The original length L (= 3.70 m) is initially at the marker position of 4.5 mm on the scale (refer to the graph on the y-axis when F = 0 N).

When the force F = 10 N, extension e = 8.0 – 4.5 = 3.5 mm = 3.5×10-3 m

Cross-sectional A = πd2 / 4

E = FL / Ae
E = 4FL / πd2e


E = 4 × 10 × 3.70 / (π × (0.25×10-3)2 × (3.5×10-3))

 
Young modulus E = 2.2×1011 Pa

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