Question:
A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of iron. Determine the ratios of their diameters if each is to have the same tension.
Answer:
Young s modulus is
Y = stress/strain = F/A/Strain = 4F/Ï€d2/Strain...(1)
Force = F
Area of cross section = A
Diameter of the wire = d
So, Y ∞ 1/d2
Young s modulus of Iron Y1 = 190 x 109 Pa
Diameter of the Iron wire = d1
Young s modulus of Iron Y2 = 110 x 109 Pa
Diameter of the Iron wire = d2
The ratio of their diameter
d2/d1 = √Y1/Y2 = √190 x 109/110 x 109 = √19/11 = 1.31:1
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