A flat horizontal board moves up and down in SHM of amplitude a. Then the shortest permissible t...

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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
\( P \) not lose contact with the board is
(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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