Note quite the "Eureka!" experiment

Level pending

A container of water is sitting on a scale. Originally, the scale reads $$M_1 = 45 \, \text{kg}$$. A block of wood is suspended from a second scale; originally the scale read $$M_2 = 12 \, \text{kg}$$. The density of wood is $$0.60 \, \text{g/cm}^3$$; the density of the water is $$1.00 \, \text {g/cm}^3$$. The block of wood is lowered into the water until half of the block is beneath the surface. Let the reading of $$M_1$$ be $$a \, \text{kg}$$. Let the reading of $$M_2$$ be $$b \, \text{kg}$$, where $$a, b$$ are integers. Compute $$ab$$.

Note: A version of this problem appeared on the 2012 F = ma exam.

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