Physics-
General
Easy

Question

A simple pendulum is suspended from the ceiling of a lift. When the lift is at rest its time period is T. With what acceleration should the lift be accelerated upwards in order to reduce its period to T divided by 2? (g is acceleration due to gravity)

  1. 2 g    
  2. 3 g    
  3. 4 g    
  4. g    

The correct answer is: 3 g


    Time period of simple pendulum is given by
    T equals 2 pi square root of fraction numerator l over denominator g end fraction end root…(i)
    When the lift is moving up with an acceleration a, then time period becomes
    T to the power of ´ end exponent equals 2 pi square root of fraction numerator l over denominator g plus a end fraction end root
    Here, T to the power of ´ end exponent equals fraction numerator T over denominator 2 end fraction
    rightwards double arrow fraction numerator T over denominator 2 end fraction equals 2 pi square root of fraction numerator l over denominator g plus a end fraction end root…(ii)
    Dividing Eq.(ii) by Eq. (i), we get
    a equals 3 g

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