Question

A force Fmakes the length of wire, 1.001 times the original length of wire of cross-section A. The Young's modulus of material of wire is
F
А
100F
А
500F
A
1000F
А​

Answer 1

Y = $\frac{F}{0.001A}$

• A solid material's tensile or compressive stiffness when a force is applied lengthwise is measured by Young's modulus, also known as the Young modulus or the modulus of elasticity in tension or compression (i.e., negative tension). It measures the relationship between axial strain (proportional deformation) and tensile/compressive stress (force per unit area) in a material's linear elastic zone.
• When a little compression or extensional load is applied to a solid material, it will deform elastically. Reversible elastic deformation means that after the force is removed, the material resumes its original shape.
• The stress-strain curve is linear at nearly zero stress and strain, and Hooke's law, which asserts that stress is proportionate to strain, describes the connection between stress and strain. Young's modulus is the proportionality coefficient. In an ideal rigid body, the Young's modulus would be infinite, meaning that greater stress was required to produce the same amount of strain. On the other hand, a very soft substance (such a fluid) would deform naturally and have no Young's modulus.
• Beyond a limited degree of distortion, few materials are linear and elastic.

Here, according to the given information, we are given that,

A force F makes the length of wire, 1.001 times the original length of wire of cross-section A.

Now, we know that,

$Y=\frac{\frac{F}{A} }{\frac{l_{1} }{l} }$

Now, $l_{1} = 1.001l - l = 0.001l$

Then, Y = $\frac{F}{0.001A}$

Hence, Y = $\frac{F}{0.001A}$.

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