AP EAMCET · PHYSICS · Mechanical Properties of Fluids

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 $(1 / 10)^{th}$ that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be

A $(\sqrt{\frac{9}{10}}) T$
B $(\sqrt{\frac{10}{9}}) T$
C $(\frac{9}{10}) T$
D Unchanged

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Correct Answer

(D) Unchanged

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Detailed explanation

When the heavy brass sphere is hung from a spring and it executes vertical vibrations with time period T, time period of oscillation of spring is, T=2πmk Now, the sphere is immersed in a non-viscous liquid with a density (1/10)th that of brass, since the time period…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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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 (1/10)th 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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