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A composite wire consists of a steel wire of length 1.5 m and a copper wire of length 2 m , with a uniform cross section area of 2.5 * 10^-5 metre square. It is loaded with a mass of 200 kg .find the extension produced . Plzzz someone help me in solving this answer as fast as possible

A composite wire consists of a steel wire of length 1.5 m and a copper wire of length 2 m , with a uniform cross section area of 2.5 * 10^-5 metre square. It is loaded with a mass of 200 kg .find the extension produced . 
Plzzz someone help me in solving this answer as fast as possible

Grade:11

1 Answers

Arun
25750 Points
4 years ago
Given-
ls = 1.5 m
lc = 2 m
Ys = 2×10^11 N/m^2
Yc = 10^11 N/m^2
m = 200 kg
A = 5.5×10^-5 m^2
# Formula-
∆l = Fl / YA
∆l = mgl / YA
# Solution-
For steel wire,
∆ls = mgls / YsA
For copper wire,
∆lc = mglc / YcA
Total extension is calculated by -
∆l = ∆ls + ∆lc
∆l = mgls/YsA + mglc/YcA
∆l = (mg/A) (ls/Ys + lc/Yc)
Substituting values -
∆l = (200×10/5.5×10^-5) (1.5/2×10^11 + 2/10^11)
∆l = (3.64×10^7) (2.75×10^-11)
∆l = 0.001 m
∆l = 1 mm
Extension produced in the wire is 1 mm.
 

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