A) \[\frac{T}{4}\]
B) \[\left( \frac{\sqrt{3}}{4} \right)T\]
C) \[\left( \frac{\sqrt{3}}{2} \right)T\]
D) \[\frac{T}{2}\]
Correct Answer: C
Solution :
Here: Acceleration of lift \[(a)=g\text{/}3\] Initial time period \[{{T}_{1}}=T\] The effective acceleration when it is ascending \[{{g}_{2}}=g-a=g-\frac{8}{3}=\frac{2g}{3}\] Time period of simple pendulum \[T=2\pi \sqrt{\frac{l}{g}}\] or \[T\propto \frac{\sqrt{1}}{g}\] Hence \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{{{g}_{2}}}{{{g}_{1}}}}=\sqrt{\frac{\frac{2}{3}g}{g}}\] or \[{{T}_{2}}=\left( \sqrt{\frac{3}{2}} \right){{T}_{1}}=\left( \sqrt{\frac{3}{2}} \right)T\]
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