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The breaking stress of a material is $10^{9}$ pascal. If the density of material is $3\times {{10}^{3}}Kg/{{m}^{3}}$. The minimum length of the wire for which it breaks under its own weight will be
(A) $3.4 \mathrm{m}$
(B) $3.4 \times 10^{4} \mathrm{m}$
(C) $3.4 \times 10^{5} \mathrm{m}$
(D) $3.4 \times 10^{3} \mathrm{m}$

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Last updated date: 22nd Jun 2024
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Answer
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Hint: We know that in physics, stress is the force acting on the unit area of a material. The effect of stress on a body is named as strain. Stress can deform the body. There are six types of stress: compression, tension, shear, bending, torsion, and fatigue. Each of these stresses affects an object in different ways and is caused by the internal forces acting on the object. The internal forces are the result of how forces are applied to an object.

Complete step by step answer
We know that breaking stress is the maximum force that can be applied on a cross sectional area of a material in such a way that the material is unable to withstand any additional amount of stress before breaking. The stress applied to a material is the force per unit area applied to the material. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress. Tensile means the material is under tension.
We should also know that it depends on nothing but the nature of the material. In the first part you may have been asked about the breaking 'force' or something like that; breaking stress is fixed. A material breaks when both the 'stress on it' and 'strain in it' increases (in fact both are related by the modulus of elasticity).
The maximum force the wire can withstand is given as $Al\rho g$
Here, A is the area, l is the length, g is the acceleration due to gravity and $\rho $is the density
or Breaking stress $=\dfrac{\text { Maximum force }}{\text { cross - sectional area }}=\dfrac{\text { ALg } \rho}{\text { A }}$
Now we have to put the values to get that:
$\mathrm{L}=\dfrac{\text { Breaking stress }}{\rho \mathrm{g}}=\dfrac{10^{9}}{3 \times 10^{3} \times 10}=3.4 \times 10^{4} \mathrm{m}$

Hence the correct answer is option B.

Note: We can conclude that strain is the change in length divided by the initial length. Stress-strain curves describe the elastic and inelastic properties of materials by showing how a material like steel responds to applied force. The uniaxial tensile test is typically used for studying stress and strain. Stress that occurs when a member is loaded by an axial force is known as normal force. In other words, when, the stress applied is perpendicular to the body. The length of body volume of the object is changed, stress will be normal. It represents the symbol $\sigma$ SI unit of Normal stress is MPa.