Oscillations

JEE Main level, single correct, medium

124 of 194

Question 124 of 194

Time period of a simple pendulum is TT inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g2\dfrac{g}{2}, the time period of pendulum will be :

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Answer: (D) 23T\sqrt{\dfrac{2}{3}}T

When lift is stationary
T=2πLgT=2\pi \sqrt{\dfrac{L}{g}}
When lift is moving upwards
⇒\Rightarrow Pseudo force acts downwards
⇒geff=g+g2=3g2\Rightarrow {g}_{eff}=g+\dfrac{g}{2}=\dfrac{3g}{2}
⇒\Rightarrow New time period
T′=2πLgeff=2π2L3g{T}^{'}=2\pi \sqrt{\dfrac{L}{{g}_{eff}}}=2\pi \sqrt{\dfrac{2L}{3g}}
T′=23T{T}^{'}=\sqrt{\dfrac{2}{3}}T

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