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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Some Mechanical Properties of Matter

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Some Mechanical Properties of Matter

Steel has an elastic limit of 8 × 10^8 N/m^2 and a Young modulus of...

Steel has an elastic limit of 8×108 N/m28 \times 10^8 \text{ N/m}^2 and a Young modulus of 2×1011 N/m22 \times 10^{11} \text{ N/m}^2. Determine the maximum elongation that can be produced in a half-metre steel wire without exceeding its elastic limit.

Options

  1. A1 mm1 \text{ mm}
  2. B4 mm4 \text{ mm}
  3. C2 mm2 \text{ mm}
  4. D8 mm8 \text{ mm}

Correct answer

C. 2 mm2 \text{ mm}

Step-by-step solution

Given:

Elastic limit (maximum stress), σ=8×108 N/m2\sigma = 8 \times 10^8 \text{ N/m}^2

Young's modulus, Y=2×1011 N/m2Y = 2 \times 10^{11} \text{ N/m}^2

Length of the wire, L=0.5 mL = 0.5 \text{ m}

From the definition of Young's modulus:

Y=StressStrain=σΔL/LY = \dfrac{\text{Stress}}{\text{Strain}} = \dfrac{\sigma}{\Delta L / L}

Rearranging for maximum elongation ΔL\Delta L:

ΔL=σ×LY\Delta L = \dfrac{\sigma \times L}{Y}

Substituting the given values:

ΔL=8×108×0.52×1011\Delta L = \dfrac{8 \times 10^8 \times 0.5}{2 \times 10^{11}}

ΔL=4×1082×1011\Delta L = \dfrac{4 \times 10^8}{2 \times 10^{11}}

ΔL=2×10−3 m\Delta L = 2 \times 10^{-3} \text{ m}

ΔL=2 mm\Delta L = 2 \text{ mm}
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