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A massless rod B D of length l is suspended by two identical massless strings A B and C D of equal lengths. A block of mass m is suspended from a point P such that B P is equal to x . If the fundamental frequency of the left wire is twice of the fundamental frequency of right wire, then the value of x is

Options

  1. Al ⁡ / 5
  2. Bl ⁡ / 4
  3. C4 l ⁡ / 5
  4. D3 l ⁡ / 4

Correct answer

A. l ⁡ / 5

Step-by-step solution

f ⁡ ∝ v ⁡ ∝ T ⁡ f ⁡ AB = 2 f ⁡ CD ∴ T AB = 4 T CD     . . . ( 1 ) Further Σ τ p = 0 ∴ T AB x = T CD ℓ - x or 4 x = l ⁡ - x T AB = 4 T CD or x = l ⁡ / 5

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