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The length of a metal wire is l 1 when the tension in it is T 1 and is l 2 when the tension is T 2 . The natural length of wire is

Options

  1. Al 1 + l 2 2
  2. Bl 1 l 2
  3. Cl 1 T 2 - l 2 T 1 T 2 - T 1
  4. Dl 1 T 2 + l 2 T 1 T 2 + T 1

Correct answer

C. l 1 T 2 - l 2 T 1 T 2 - T 1

Step-by-step solution

Let the original length be l . In first case, l 1 = l + d l 1 Using Hooke's law, x = T K Where, x is the displacement. We have, l 1 = l + T 1 K ... (i) Similarly, l 2 = l + T 2 K ... (ii) Solving Equations. (i) and (ii), we get l = l 1 T 2 - l 2 T 1 T 2 - T 1

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