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

A heavy but uniform rope of length L is suspended from a ceiling. If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceiling?

Options

  1. AL g
  2. BL 2g
  3. C4L g
  4. D2L g

Correct answer

C. 4L g

Step-by-step solution

Let the mass of the rope be M and its length be L . The linear mass density is = M L . Consider a point at a distance x from the bottom of the rope. The tension T at this point is due to the weight of the rope below it. T = ( x) g The speed of the transverse pulse at a distance x from the bottom is given by: v = T = x g = gx Since v = dx dt , we have: dx dt = gx dt = dx gx Integrating both sides to find the total time t taken by the pulse to travel from the bottom ( x = 0 ) to the ceiling ( x = L ): t = ₀^ L dx gx

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