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A uniform vertical cylinder of cross-sectional area A floats, 90 $%$ submerged in an unknown liquid inside a tank with cross-sectional area four times that of cylinder When cylinder is pushed down gently by x , the liquid comes up by $x_{1}$ w.r.t. the original level. Then the ratio of x to $x_{1}$ will be______.

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Solution

Cylinder can perform SHM only till it is partially submerged. When cylinder goes down by x inside
the liquid level comes up by $x_{1}$ ,

(4a-a) $x_{1}$ =xa

$\Rightarrow$ $x_{1}$ = $\frac{x}{3}$

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