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Simple Harmonic Motion — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsSimple Harmonic Motion1 Mark
Question
Assertion : The frequency of a second pendulum in an elevator moving up with an acceleration half the acceleration due to gravity is $0.612 s$.
Reason : The frequency of a second pendulum does not depend upon acceleration due to gravity.
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Answer

(c) Frequency of second pendulum $n=(1 / 2) s^{-1}$. When elevator is moving upwards with acceleration $g / 2$, the effective acceleration due to gravity is$g=g+a=g+g / 2=3 g / 2 .$As $n=\frac{1}{2 \pi} \sqrt{\frac{g}{l}}$ so $n^2 \propto g$.$\begin{aligned}& \therefore \frac{n_1^2}{n_2^2}=\frac{g_1}{g}=\frac{3 g / 2}{g}=\frac{3}{2} \text { or, } \frac{n_1}{n}=\sqrt{\frac{3}{2}}=1.225 \\& \text { or, } n_1=1.225 n=1.225 \times(1 / 2)=0.612 \mathrm{~s}^{-1} .\end{aligned}$

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