The Time-keeper

A man sits on the inner side of a hollow sphere and measures the seconds as they pass. Find the time (in \(\si{\second}\)) he measures during one oscillation of the pendulum.

Details and Assumptions

  • Length of string is \(l=1 \text{ m}\)
  • Radius of sphere is \(R=1 \text{ m}\)
  • String is attached at point \(P\) and man sits diametrically opposite to this point.
  • Masses of both man and sphere are same.
  • The man doesn't slip on the sphere ie., he sits at the same point on the sphere.

  • Assume the figure at the bottom of the sphere to be the man.

  • The oscillations take place in uniform gravitational field where \(g = 9.81 \) SI units.

This problem is part of the set innovative problems in mechanics.

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