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STD 11 - 13. oscillations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 13. oscillations4 Marks
MCQ
A flat horizontal board moves up and down under $S.H.M.$ vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is ..........
  • A
    $2 \pi \sqrt{\frac{g}{A}}$
  • ✓
    $2 \pi \sqrt{\frac{A}{g}}$
  • C
    $2 \pi \sqrt{\frac{2 A}{g}}$
  • D
    $\frac{\pi}{2} \sqrt{\frac{A}{g}}$
✓

Answer

Correct option: B.
$2 \pi \sqrt{\frac{A}{g}}$
b
(b)

Maximum acceleration of the system $\left(a_{\max }\right)=-\omega^2 A$

For a block to escape the board the acceleration must be equal to 9 at the top-most point.

$g=\omega^2 A$

$\omega=\sqrt{\frac{g}{A}}$

Time period $=\frac{2 \pi}{\omega}=\sqrt{\frac{A}{g}}$

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