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MHT CET202310 May 2023Evening ShiftPhysicsWaves and SoundActual

A uniform rope of length ' L ' and mass ' m ₁ ' hangs vertically from a rigid support. A block of mass ' m ₂ ' is attached to the free end of the rope. A transverse wave of wavelength ' ₁ ' is produced at the lower end of the rope. The wavelength of the wave when it reaches the top of the rope is ' ₂ '. The ratio ₁ ₂ is

Options

  1. A[ m ₂ ~m ₁+ m ₂ ]^ 1 2
  2. B[ m ₁+ m ₂ ~m ₂ ]^ 1 2
  3. C[ m ₁ ~m ₁+ m ₂ ]^ 1 2
  4. D[ m₂ m₁-m₂ ]^ 1 2

Correct answer

A. [ m ₂ ~m ₁+ m ₂ ]^ 1 2

Step-by-step solution

Let velocity of pulse at lower end be v₁ and at top be v ₂ ₂ ₁ = v ₂ v ₁ ( = v n and n = constant ) Velocity of transverse wave on a string is v = T m where, m is linear density. In this case, v T ₂ ₁ = v ₂ v ₁ = T ₂ ~T ₁ = ( m ₂+ m ₁ ) m ₂ Where, T₂ is tension at upper end of rope and T₁ is tension at lower end of rope. ₁ ₂ = m₂ m₂+m₁

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