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Question: Longitude stress of \(1kgm{{m}^{-2}}\) is applied on a wire. The percentage increase in length is (Y...

Longitude stress of 1kgmm−21kgm{{m}^{-2}} is applied on a wire. The percentage increase in length is (Y= 1011Nm−2{{10}^{11}}N{{m}^{-2}})
A.) 0.002
B.) 0.001
C.) 0.003
D.) 0.01

Explanation

Solution

We know that Young’s Modulus is a measure of elasticity, it is defined as the ratio of the stress acting on a substance to the strain produced. It is a mechanical property and its symbol is (Y). The basic principle on which it is based is that when we remove the force how fast the object attains its original shape and size.

Formula Used:
Y=StressStrainY=\dfrac{Stress}{Strain}
Strain=ΔLLStrain=\dfrac{\Delta L}{L}

Complete Step by Step Solution:
In the above question we are given with longitudinal stress which is defined as force per unit area and we have given the value of young’s modulus for that wire.
First, we will write down all the given quantities.
Young’s modulus (Y)= 1011Nm−2{{10}^{11}}N{{m}^{-2}}
longitudinal Stress = 1kgmm−21kgm{{m}^{-2}}
we need to find out the strain in order to find out the percentage change in length.

We know the formula, Y=StressStrainY=\dfrac{Stress}{Strain}
Putting the values in this we get, 1011Nm−2=1kgmm−2Strain{{10}^{11}}N{{m}^{-2}}=\dfrac{1kgm{{m}^{-2}}}{Strain}
strain=1kgmm−21011Nm−2strain=\dfrac{1kgm{{m}^{-2}}}{{{10}^{11}}N{{m}^{-2}}}

But we need to convert the mm2m{{m}^{2}}into m2{{m}^{2}} for that we need to know he conversion formula
1 mm2m{{m}^{2}}= 1×10−6m21\times {{10}^{-6}}{{m}^{2}}

Putting thus conversion into above formula we get,
strain=1105strain=\dfrac{1}{{{10}^{5}}} kgN−1kg{{N}^{-1}}

Now we know that Strain=ΔLLStrain=\dfrac{\Delta L}{L}
Strain=ΔLL=1105Strain=\dfrac{\Delta L}{L}=\dfrac{1}{{{10}^{5}}}

To find the percentage change in L we need to multiply this by 100
ΔLL=1105×100\dfrac{\Delta L}{L}=\dfrac{1}{{{10}^{5}}}\times 100
We will get ΔL=0.001\Delta L=0.001%

Hence, we can conclude that option (B) is the correct answer for the above question.

Note:
Stress is defined as the force per unit area while strain is defined as the change or extension or elongation per unit length. Strain does not have any units; it is basically measured in percentage or ratio. The ratio of stress to the strain is defined as young’s modulus which shows how elastic a material is.