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A steel rail of length 5 m and area of cross section 40 cm 2 is prevented from expanding along its length while the temperature rises by 10 ° C . If coefficient of linear expansion and Young's modulus of steel are 1.2 × 10 - 5 K - 1 and 2 × 10 11 N m - 2 respectively, the force developed in the rail is approximately:

Options

  1. A2 × 10 7   N
  2. B2 × 10 9   N
  3. C3 × 10 - 5   N
  4. D1 × 10 5   N

Correct answer

D. 1 × 10 5   N

Step-by-step solution

F = Y A α Δ t ⇒ F = 2 × 10 11 × 40 × 10 - 4 × 1.2 × 10 - 5 × 10 ⇒ F = 9.6 × 10 4 ≈ 1 × 10 5   N .

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