A steel wire of cross-sectional area 3 ×10^-6 m^2 can with stand a maximum strain of 10^-3 Youn

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A steel wire of cross-sectional area 3 ×10^-6 m^2 can with...

A steel wire of cross-sectional area $3 \times 10^{-6} \mathrm{~m}^{2}$ can with stand a maximum strain of $10^{-3}$ Young's modulus of steel is $2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)$. The maximum mass the wire can hold is..... $\left[\mathrm{g}=10\left(\mathrm{~m} / \mathrm{s}^{2}\right)\right]$ (A) $40 \mathrm{~kg}$ (B) $60 \mathrm{~kg}$ (C) $80 \mathrm{~kg}$ (D) $100 \mathrm{~kg}$

A steel wire of cross-sectional area $3 \times 10^{-6} \mathrm{~m}^{2}$ can with stand a maximum strain of $10^{-3}$ Young's modulus of steel is $2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)$. The maximum mass the wire can hold is..... $\left[\mathrm{g}=10\left(\mathrm{~m} / \mathrm{s}^{2}\right)\right]$
(A) $40 \mathrm{~kg}$
(B) $60 \mathrm{~kg}$
(C) $80 \mathrm{~kg}$
(D) $100 \mathrm{~kg}$

Key Concepts

Load and Weight Calculation

Load and weight calculation involves determining the force exerted by a mass under the influence of gravity, using the relation F = mg. This concept is used to understand how much load or mass a structure or material can support without exceeding its mechanical limits.

Cross-sectional Area

The cross-sectional area of a material refers to the area of its cross-section that is perpendicular to the direction of the applied force. It is crucial in determining the stress experienced by the material, as stress is calculated by dividing the force by this area.

Hooke's Law

Hooke's Law states that, within the elastic limit of a material, the deformation (strain) is directly proportional to the applied force (stress). This principle underlies the linear relationship expressed by Young's modulus and is essential for predicting material behavior under load.

Strain

Strain is the measure of the relative change in dimensions of a material when subjected to stress, defined as the ratio of deformation (change in length) to the original length. It is a dimensionless quantity and helps in assessing how much a material deforms under a given load.

Stress

Stress is the force applied per unit area over a material, and it provides a measure of the internal forces that develop within the material in response to an external load. It is typically measured in pascals (N/m²) and is a fundamental concept in understanding how materials bear loads.

Young's Modulus

Young's modulus is a material property that quantifies the relationship between stress and strain in the elastic region of a material's deformation. It is defined as the ratio of stress to strain and indicates the stiffness of the material; a higher value signifies a stiffer material.

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