A 4m long wire of radius 4 mm is elongated by 0.01% when loaded by a force of 80π newton. What is the stress in the wire and Young's modulus of wire?

Solution

Length of the wire, l = 4m
Radius of the wire, r = 4 mm = 0.004 m
Force on the wire, F = 80 $π N$
Strain = 0.01% = 0.0001

Now, using the formula of stress,

$Stress = \frac{F}{{πr}^{2}}$ = $\frac{80 π}{π (0.004)^{2}} = 5 \times 10^{6} N / m^{2}$

Young's modulus of the wire is given by,
Y = $\frac{Stress}{Strain} = \frac{5 \times 10^{6}}{0.0001} = 5 \times 10^{10} N / m^{2}$

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Mechanical Properties Of Fluids

A 4m long wire of radius 4 mm is elongated by 0.01% when loaded by a force of 80π newton. What is the stress in the wire and Young's modulus of wire?

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