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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 lift be accelerated upwards in order to reduce its time period to T/2?
  1. -3g
  2. g
  3. 2g
  4. 3g

A
g
B
-3g
C
2g
D
3g
Solution
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We know T=2πlg.
Thus, T is inversely proportional to square root of g.
For, time period to become T/2, we have geff=4g beacause 2πl4g=T/2
Thus, to get geff=4g, lift should be moving upward with 3g, so that net acceleration of pendulum should be 3g(downward due to pseudo force)+g(downward due to gravity)=4g

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