A) \[\frac{T}{3}\]
B) 3T
C) \[\frac{\sqrt{3}T}{2}\]
D) \[\sqrt{\frac{3}{2}}T\]
Correct Answer: C
Solution :
Time period of simple pendulum \[\operatorname{T}=2\pi \sqrt{\frac{l}{{{g}_{eff}}}}\] \[\operatorname{T}=2\pi \sqrt{\frac{l}{g}}\] When lift stationary When lift starts moving upwards with an acceleration\[\frac{g}{3}\] \[\operatorname{T}=2\pi \sqrt{\frac{l}{g+a}}\] \[\operatorname{a}=\frac{g}{3}\] \[\operatorname{T}''=2\pi \sqrt{\frac{l}{g+\frac{g}{3}}}=2\pi =\sqrt{\frac{3\operatorname{l}}{4\operatorname{g}}}\] \[\operatorname{T}''=\frac{\sqrt{3}}{2}\operatorname{T}\]
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