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A heavy brass sphere is hung from a spring and it executes vertical vibrations with period T. The sphere is now immersed in a non-viscous liquid with a density ${(1 / 15)}^{t h}$ that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be

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Unchanged

$(\sqrt{\frac{14}{15}}) T$

$(\frac{14}{15}) T$

$(\sqrt{\frac{15}{10}}) T$

answer is D.

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Detailed Solution

$ρ_{l} = \frac{ρ_{b}}{15}$

$m g - F_{b} = m g^{1}$

$m g - V \frac{ρ_{b}}{15} g = m g^{1}$

$m g^{1} = m g - \frac{m g}{15} = \frac{14 m g}{15}$

$g^{1} = \frac{14}{15} g$ ….. (1)

$T^{1} = 2 π \sqrt{\frac{m}{k}}$

Time period of spring does no depends on $' g'$ . So, T does not change.

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