The ratio, (density of a floating object) : (density of liquid) equals the fraction of the floating object by volume that is immersed in the liquid.
Newton's Second and Third laws are used to explain how a spring balance works.
The (true) weight W of an object is the force of gravity on the object and thus is constant.
The apparent weight (reading on balance) of an object immersed in a liquid is W - B where B is the buoyancy of the object.
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