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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
The period of small oscillation of a simple pendulum is $T$. The ratio of density of liquid to the density of material of the bob is $\rho \left( {\rho  < 1} \right)$.When immersed in the liquid, the time period of small oscillation will now be
  • A
    $T$
  • B
    $T\left( {1 - \rho } \right)$
  • ✓
    $\frac{T}{{\sqrt {1 - \rho} }}$
  • D
    $T\sqrt {1 - \rho } $
✓

Answer

Correct option: C.
$\frac{T}{{\sqrt {1 - \rho} }}$
c
${\rm{T}} = 2\pi \sqrt {\frac{l}{{\rm{g}}}} $

when immerge in liquid

$\mathrm{mg}^{\prime}=\mathrm{mg}-\mathrm{F}_{\mathrm{up}}$

${{\rm{g}}^\prime } = {\rm{g}} - \frac{{{\rm{v}}{{\rm{d}}_l}{\rm{g}}}}{{{\rm{v}}{{\rm{d}}_0}}}$

$g^{\prime}=g(1-\rho)$

${{\rm{T}}^\prime } = 2\pi \sqrt {\frac{l}{{{\rm{g}}(1 - \rho )}}} $

$\frac{{T'}}{T} = \frac{1}{{\sqrt {1 - \rho } }} \Rightarrow {T^\prime } = \frac{T}{{\sqrt {1 - \rho } }}$

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