We all have done this!

The situation in the question has been experimented my most of us in our childhood, but no one probably thought of this!

There is a thread of mass \(M\) and length \(L\) is stretched on a smooth horizontal surface with constant forces acting on either sides of the rope. A sudden movement causes the rope to form a circular loop traveling traveling from one end of the rope, with constant velocity \(v\).


  • \(v\) is the velocity of the loop.
  • \(\ell\) is the angular momentum of the moving loop about the centre of the loop.
  • \(KE\) is the Kinetic Energy of the loop.

Evaluate \(\large |v| + |\ell| + |KE|\). Give your answer to 3 decimal places.


  • Take \(M = 5kg,~ L = 3m,~F = 7N\)
  • Radius of the loop, \(R = 10 cm\)
  • There is no gravitational field.

This is an not an original question.

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