A flat horizontal board moves up and down in SHM of amplitude \( a ...

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A flat horizontal board moves up and down in SHM of amplitude \( a \). Then the shortest permissible time period of the vibration such that an object placed on the board may
\( \mathrm{P} \) not lose contact with the board is

W
(A) \( 2 \pi \sqrt{\frac{g}{a}} \)
(B) \( 2 \pi \sqrt{\frac{a}{g}} \)
(C) \( 2 \pi \sqrt{g \times a} \)
(D) \( \frac{1}{2 \pi} \sqrt{\frac{g}{a}} \).
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