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  4. A test tube with some lead shots in it has a total mass M. It floats upright in a liquid of density d. The crosssectional area of the tube is A. It is pressed slightly downwards from position of stable equilibrium and released. It executes SHM with a period of

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Q. A test tube with some lead shots in it has a total mass $M$. It floats upright in a liquid of density $d$. The crosssectional area of the tube is $A$. It is pressed slightly downwards from position of stable equilibrium and released. It executes SHM with a period of

Oscillations

Solution:

$F=-(A x) d g$
or $F=-(A d g) x$
$ \Rightarrow k=A d g$
$ \Rightarrow T=2 \pi \sqrt{\frac{m}{k}}=2 \pi \sqrt{\frac{M}{A g d}}$