Is the oscillation of a simple pendulum at the centre of the earth be possible ?

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No, because the value of $g$ at the centre of earth is zero and hence, in periodic time $\mathrm{T}=2 \pi \sqrt{\frac{l}{g}}$ now put $g=0$

$\therefore \mathrm{T}=2 \pi \sqrt{\frac{l}{0}}=$ infinite

Means oscillation does not occurs.

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