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When a metallic wire is held under a tensile force F 1 , the length of the wire is L 1 . If the force is changed to F 2 , the length of the wire is L 2 . The original length L of the wire is

Options

  1. AL 1 F 1 + L 2 F 2 F 1 + F 2
  2. BL 2 - L 1 F 1 + F 2
  3. CF 1 L 2 - F 2 L 1 F 1 - F 2
  4. DF 1 L 1 - F 2 L 2 F 1 - F 2

Correct answer

C. F 1 L 2 - F 2 L 1 F 1 - F 2

Step-by-step solution

F ∝ d l F 1 ∝ L 1 - l ⇒       ( 1 ) F 2 ∝ L 2 - l ⇒     ( 2 ) F 1 F 2 = L 1 - l L 2 - l F 1 L 2 - F 1 l = F 2 L 1 - F 2 l F 1 - F 2 l = F 1 L 2 - F 2 L 1 l = F 1 L 2 - F 2 L 1 F 1 - F 2

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