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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