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NEET2026PhysicsChapterActual

A structural steel cable of length 5 m and cross-sectional area 4 10⁻⁴ m ^2 is rigidly clamped at both ends between two massive pillars. The cable is initially at a temperature of 40^ C . If the temperature of the surroundings drops to 15^ C , what is the tension developed in the cable? (Given: Young's modulus of steel = 2.0 10¹¹ N m ⁻² , coefficient of linear expansion of steel = 1.2 10⁻⁵ , ^ C ⁻¹ )

Options

  1. A1.2 10^5 N
  2. B2.4 10^4 N
  3. C4.8 10^3 N
  4. D3.84 10^4 N

Correct answer

B. 2.4 10^4 N

Step-by-step solution

Given: A = 4 10⁻⁴ m ^2 T = 40^ C - 15^ C = 25^ C Y = 2.0 10¹¹ N m ⁻² = 1.2 10⁻⁵ , ^ C ⁻¹ The thermal stress developed in the cable is given by Y T . The tension F developed in the cable is: F = Y A T Substituting the values: F = (2.0 10¹¹) (4 10⁻⁴) (1.2 10⁻⁵) 25 F = 240 10^2 N F = 2.4 10^4 N Answer: 2.4 10^4 N

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