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NDA 1 2024 GAT, question 87

Topic: Physics

Q87

Which one of the following statements regarding simple pendulum is correct ?

Simple pendulum has a time period independent of amplitude :

  1. (a) only for small amplitudes because then the net force on its bob is independent of its displacement.
  2. (b) for any amplitude because the net force on the bob is always proportional to its displacement.
  3. (c) for any amplitude because the net force on the bob is independent of its displacement.
  4. (d) only for small amplitudes because then the net force on its bob is proportional to its displacement.Correct answer

Solution.

Answer: (d) only for small amplitudes because then the net force on its bob is proportional to its displacement.

  1. For small angles, sin θ ≈ θ, so the tangential restoring force −mg sin θ is proportional to displacement and opposite in direction.
  2. This gives approximately simple harmonic motion with an amplitude-independent period.
  3. The approximation fails at large amplitudes.