A heavy brass sphere is hung from a light spr | vedclass

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(B) The period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$.When the sphere is immersed in a liquid,it experiences an upward buoy

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$(9/10)^{1/2}T$

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(B) The period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$.When the sphere is immersed in a liquid,it experiences an upward buoyant force $F_B = V\rho_L g$,where $V$ is the volume of the sphere and $\rho_L$ is the density of the liquid.The effective weight of the sphere becomes $W_{eff} = mg - F_B = V\rho_S g - V\rho_L g = Vg(\rho_S - \rho_L)$,where $\rho_S$ is the density of the sphere.Since $\rho_L = \frac{1}{10}\rho_S$,the effective weight is $W_{eff} = Vg(\rho_S - \frac{1}{10}\rho_S) = Vg(\frac{9}{10}\rho_S) = \frac{9}{10}mg$.This is equivalent to a system with an effective mass $m' = \frac{9}{10}m$.The new period $T'$ is $T' = 2\pi \sqrt{\frac{m'}{k}} = 2\pi \sqrt{\frac{9m}{10k}} = \sqrt{\frac{9}{10}} T = \sqrt{\frac{9}{10}} T$.

$A$ heavy brass sphere is hung from a light spring and is set in vertical small oscillations with a period $T$. The sphere is now immersed in a non-viscous liquid with a density $1/10$th the density of the sphere. If the system is now set in vertical $S.H.M.$,its period will be

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