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13.Oscillations
hard
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
$T\left( {1 - \rho } \right)$
C
$\frac{T}{{\sqrt {1 - \rho} }}$
D
$T\sqrt {1 - \rho } $
Solution
${\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 )}}} $
$\frac{{T'}}{T} = \frac{1}{{\sqrt {1 – \rho } }} \Rightarrow {T^\prime } = \frac{T}{{\sqrt {1 – \rho } }}$
Standard 11
Physics
