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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 x1 w.r.t. the original level. Then the ratio of x to x1 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 x1,

(4a-a)x1=xa

x1 = x3


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