A uniform cube of density ρ/2 floats in a liquid of density ρ. A small vertical downward displacement x is given and the cube is released without damping. If its horizontal cross-sectional area is A and side is l, its angular frequency is:
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Question

A uniform cube of density ρ/2 floats in a liquid of density ρ. A small vertical downward displacement x is given and the cube is released without damping. If its horizontal cross-sectional area is A and side is l, its angular frequency is:

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G1 Physics · Accepted Answer

A downward displacement x adds buoyancy ρgAx, so restoring constant k=ρgA. Cube mass=(ρ/2)Al. Thus ω²=k/m=ρgA/[(ρ/2)Al]=2g/l, giving ω=√(2g/l).