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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
A flat horizontal board moves up and down in $SHM$ of amplitude $\alpha$. Then 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}{\alpha }} $
  • ✓
    $2\pi \sqrt {\frac{\alpha}{g }} $
  • C
    $2\pi \sqrt {g \times \alpha } $
  • D
    $\frac{1}{{2\pi }}\sqrt {\frac{g}{\alpha }} $
✓

Answer

Correct option: B.
$2\pi \sqrt {\frac{\alpha}{g }} $
b
$\mathrm{m} \alpha \omega^{2}=\mathrm{mg}$

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

$\frac{2 \pi}{\mathrm{T}}=\sqrt{\frac{\mathrm{g}}{\alpha}} \quad \text { or } \quad \mathrm{T}=2 \pi \sqrt{\frac{\alpha}{\mathrm{g}}}$

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