A rope AB of length L lies on a smooth horizontal surface and is pulled by a horizontal force F at end B. The rope mass is m. If a transverse wave travels from A to B in time T, find 9T²F/(mL).
Options

Question

A rope AB of length L lies on a smooth horizontal surface and is pulled by a horizontal force F at end B. The rope mass is m. If a transverse wave travels from A to B in time T, find 9T²F/(mL).

G1 Physics · Accepted Answer

Step 1: For a uniformly massive rope pulled at one end, the local tension increases linearly from the free end. Step 2: Using v(x)=√[T(x)/μ] and integrating Ttravel = ∫dx/v gives T = 2√(mL/F). Step 3: 9T²F/(mL) = 9×4 = 36. Final: B.