A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young’s modulus for the material of the wire.

A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young’s modulus for the material of the wire.

[Take g = 10 ms−2]
A. 2.4×1010(Nm−2)
B. 1.5×1010(Nm−2)
C. 2.4×109(Nm−2)
D. 1.3×1010(Nm−2)

Correct Option: Answer is A
Young’s modulus (Y) can be calculated using Hooke’s Law, which is given by the formula:
Y =Stress/Strain
The strain (ε) is given by the formula:
ε =Extension/Original length
In this case, the extension is given as 0.5% of the original length, and the stress (σ) can be calculated using the formula:
σ =Force/Area
The force (F) can be calculated using the weight of the load (W):
F=m⋅g
where:
• m is the mass of the load (given as 1.5 kg),
• g is the acceleration due to gravity (given as 10 m/s²).
The area (A) of the wire can be calculated using the formula for the area of a circle (A=πr2), where r is the radius of the wire.
Once you have the stress and strain, you can substitute these values into the formula for Young’s modulus.
Let’s go step by step:
1. Calculate the force (F): �=1.5 kg*10 m/s2 ; F=15 N
2. Calculate the area (A): A =π⋅(0.2mm)2 => A =π⋅(0.0002m)2 A≈1.2566×10−7 m2
3. Calculate the stress (σ): σ =15 N/1.2566×10−7 ≈1.193×108 N/m2
4. Calculate the strain (ε)=0.5%100 ε=0.005
5. Finally, calculate Young’s modulus (Y): Y=1.193×108 N/m20.005Y=0.0051.193×108N/m2 Y≈2.386×1010 N/m2
A. 2.4×10^10 N/m²

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