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Mechanical Properties of Solids · NEET Preparation Physics

The breaking stress of a material is 10^8 text{ N/m}^2. Find the maximum length of a wire of this material which can be suspended vertically without…

Practice question from Mechanical Properties of Solids (NEET Preparation Physics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-0CBF3C

The breaking stress of a material is 108 N/m210^8 \text{ N/m}^2. Find the maximum length of a wire of this material which can be suspended vertically without breaking. (Density of the material ρ=2×103 kg/m3\rho = 2 \times 10^3 \text{ kg/m}^3, g=10 m/s2g = 10 \text{ m/s}^2)

  1. A.5×103 m5 \times 10^3 \text{ m}Correct answer
  2. B.104 m10^4 \text{ m}
  3. C.2×103 m2 \times 10^3 \text{ m}
  4. D.5×104 m5 \times 10^4 \text{ m}

Solution

The maximum stress experienced by the wire at its upper end due to its own weight is given by σmax=MgA=(ALρ)gA=Lρg\sigma_{\text{max}} = \frac{Mg}{A} = \frac{(AL\rho)g}{A} = L\rho g. Therefore, L=σmaxρg=1082×103×10=1082×104=5×103 mL = \frac{\sigma_{\text{max}}}{\rho g} = \frac{10^8}{2 \times 10^3 \times 10} = \frac{10^8}{2 \times 10^4} = 5 \times 10^3 \text{ m}.

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