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An iron load of 2 kg is suspended in the air from the free end of a sonometer wire of length 1 m . A tuning fork of frequency 256 Hz is in resonance with 1 7 times the length of the sonometer wire. If the load is immersed in water, the fraction of length of the wire that will be in resonance with the same tuning fork, will be (specific gravity of iron = 8 ) (assume both cases in same harmonic)

Options

  1. A8
  2. B6
  3. C1 6
  4. D1 8

Correct answer

D. 1 8

Step-by-step solution

We know l ∝ T ∴ ι air ι water = T air T water But specific gravity x = 8 T ⁡ air ⁡ = m ⁡ g ⁡ , T ⁡ water = mg 1 - 1 x = 7 8 mg ⇒ T water = 7 8 T air ∴ l air l water = 8 7 But l air = 1 7 l (Given) ∴ l water = 1 8 l

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