# A simple pendulum attached to ceiling of lift has time period T when lift is at rest.

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A simple pendulum attached to ceiling of lift has time period T when lift is at rest. Find its time period of lift if it starts accelerating upwards with acceleration g/2?

1. $$\sqrt {2\over 3} T$$
2. $${\sqrt 2\over 3} T$$
3. $${2\over \sqrt 3} T$$
4. $$T\over 3$$

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The correct option is 1) $$\sqrt{2\over 3}T$$

$$T=2\pi{ l\over g}$$

$$T'=2\pi{ l\over g+{g\over2}}$$

$$\therefore {T'\over T}={ \sqrt { g\over{ 3g \over2}}}$$

$$T'=T{\sqrt 2\over3}$$