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Q.

A pendulum suspended from the roof of an elevator at rest has a time period T₁. When the elevator moves up with an acceleration its time period becomes T₂. When the elevator moves down with same acceleration its time period becomes T₃, then

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a

$T_{1} = \frac{\sqrt{2} T_{2} T_{3}}{\sqrt{T_{2}^{2} + T_{3}^{2}}}$

b

$T_{1} = \sqrt{(T_{3} T_{2})}$

c

$T_{3} = \sqrt{(T_{1}^{2} + T_{2}^{2})}$

d

$T_{1} = \frac{T_{2}^{2}}{T_{3}}$

answer is C.

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Detailed Solution

$T∝ \frac{1}{\sqrt{g}}$

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A pendulum suspended from the roof of an elevator at rest has a time period T1. When the elevator moves up with an acceleration its time period becomes T2. When the elevator moves down with same acceleration its time period becomes T3, then