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# A Steel Wire Having Cross Sectional Area 1.5 Mm2 When Stretched by a Load Produces a Lateral Strain 1.5 X 10^-5. Calculate the Mass Attached to the Wire. - Physics

ConceptDefinition of Stress and Strain

#### Question

A steel wire having cross sectional area 1.5 mm2 when stretched by a load produces a lateral strain 1.5 x 10-5. Calculate the mass attached to the wire.

(Ysteel = 2 x 1011 N/m2, Poisson’s ratio σ = 0.291,g = 9.8 m/s2)

#### Solution

Given that A = 1.5 mm2, lateral strain = 1.5 *10−5,

Ysteel = 2 * 1011 N/m2, σ = 0.291 and g = 9.8 m/s2

Poisson's ratio, σ ="Lateral strain"/"Longitudinal strain"

∴Longitudinal strain = (1.5*10^-5)/0.291=5.14*10^-5

Longitudinal stress = Y * Longitudinal strain

=2*1011*5.14*10-5

∴Longitudinal stress =10.28*106

But longitudinal stress =(mg)/A

→10.28*106 = (M*9.8)/(1.5*10^-6)

∴M =(10.28*10^6*1.5*10^-6)/9.8=15.42/9.8

∴M = 1.58kg

Is there an error in this question or solution?

#### APPEARS IN

2015-2016 (March) (with solutions)
Question 4.4 | 3.00 marks

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Solution A Steel Wire Having Cross Sectional Area 1.5 Mm2 When Stretched by a Load Produces a Lateral Strain 1.5 X 10^-5. Calculate the Mass Attached to the Wire. Concept: Definition of Stress and Strain.
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