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BITSAT2018PhysicsMechanical Properties of SolidsActual

Breaking stress of a steel wire is p and the density of steel is ρ . The greatest length of steel wire that can hang vertically without breaking is

Options

  1. Ap ρ g
  2. Bp 2 ρ g
  3. C2 p ρ g
  4. DNone of these

Correct answer

A. p ρ g

Step-by-step solution

Maximum stress =   Maximum   weight     Cross - sectional   area   Now, maximum weight of steel wire = Volume × Density × g = A l ρ g where, l is the maximum length of steel wire that can hang vertically without breaking. ρ is the density of steel and A is the cross-sectional area of steel wire. ∴ Maximum stress, p = A l ρ g A = l ρ g ∴   l = p ρ g

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