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Simple Harmonic Motion — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsSimple Harmonic Motion2 Marks
Question
A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type. Find, the length of a seconds pendulum at a place where $\text{g}=\pi^2\text{m/s}^2.$
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Answer

$\text{T}=2\sec.$$\text{T}=2\pi\sqrt{\frac{\ell}{\text{g}}}$
$\Rightarrow2=2\pi\sqrt{\frac{\ell}{10}}$
$\Rightarrow\frac{\ell}{10}=\frac{1}{\pi^2}$
$\Rightarrow\ell=1\text{cm}$ $(\therefore\pi^2\approx10)$

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