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AP EAMCET20227 Jul 2022Morning ShiftPhysicsMechanical Properties of SolidsActual

Two wires made of same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If x is the increase in the length of the first wire, then the increase in the length of the second wire is

Options

  1. A1 3 x
  2. B3 x
  3. C9 x
  4. D3 x

Correct answer

B. 3 x

Step-by-step solution

As wires are of same material so both are having same young's modulus Y₁=Y₂ F₁ A₁ L₁ L₁ = F₂ A₂ L₂ L₂ F₁ L₁ L₁ A₁ = F₂ L₂ L₂ A₂ Now given, aligned L₁ & =3 L₂ and r₁=3 r₂ L₁ & =x aligned Also, F₁=F₂ So from eq. (i), we have 3 L₂ x (3 r₂ )^2 = L₂ L₂ r₂^2 L₂=3 x

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