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A rubber cord of density d , Young's modulus Y and length L is suspended vertically. If the cord extends by a length 0.5 L under its own weight, then L is

Options

  1. AY 2 d g
  2. BY d g
  3. C2 Y d g
  4. Dd g 2 Y

Correct answer

B. Y d g

Step-by-step solution

∵ Young's modulus Y = S t r e s s S t r a i n Y = F A ∆ L L ⇒ ∆ l = F L A Y extennsion in d x at ‘ x ’ d e = x d A g d x A Y total extension e = ∫ 0 L x d A g d x A Y = d g Y L 2 2 0.5 L = d g L 2 Y 2 ⇒ L = Y d g

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