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Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

As depicted in the figure, both strings are composed of the same material and share the same cross section. The pulleys are assumed to be light. If the transverse wave speed in string AB is v₁ and in string CD is v₂ , then the ratio v₁/v₂ is

Options

  1. A1/ 2
  2. B2
  3. C2
  4. D1

Correct answer

A. 1/ 2

Step-by-step solution

Let the tension in the string AB be T₁ and the tension in the string CD be T₂ . Since the pulley B is light (massless), the net force acting on it must be zero. The string AB passes around pulley B , so there are two upward segments of this string supporting the pulley, each exerting a force T₁ . The string CD pulls downwards on the axle of the pulley with tension T₂ . Balancing the forces on pulley B , we get: 2T₁ = T₂ T₁ T₂ = 1 2 The speed of a transverse wave in a string is given by v = T , where T is the tensio

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