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Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion

A simple pendulum of length l is attached to the ceiling of an elevator. Determine the time period of small oscillations if the elevator is going up with an acceleration a₀ .

Options

  1. A2 l g - a₀
  2. B2 l g
  3. C2 l g^2 + a₀^2
  4. D2 l g + a₀

Correct answer

D. 2 l g + a₀

Step-by-step solution

In the frame of reference of the elevator accelerating upwards with an acceleration a₀ , a pseudo force ma₀ acts downwards on the pendulum bob of mass m . The true gravitational force mg also acts downwards. The effective weight of the bob is W_ eff = mg + ma₀ = m(g + a₀) . The effective acceleration due to gravity is g_ eff = g + a₀ . The time period of a simple pendulum is given by T = 2 l g_ eff . Substituting the value of g_ eff , we get T = 2 l g + a₀ .

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