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’ w.r.t. the original level. Then the ratio of x to x’ will be ___

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 $x^1$
$(4a-a)x^1=xa\Rightarrow x^1=\frac{x}{3}$