Question

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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Answer 1

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

$\Rightarrow$ $x_1$ = $\frac{x}{3}$