Meaningless question, so unanswerable.
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Half a kilogram is the mass in this case.Half a kilogram is the mass in this case.Half a kilogram is the mass in this case.Half a kilogram is the mass in this case.
Anything that is physically there (rocks, empty boxes, dog, water, air, inflated balloons etc) has mass.
mass fraction of Substance A = (mass of Sub. A) / (total mass)
OK, we have you surrounded now! Where is the third gold bar?
The volume will be reduced to a half of its original value. If the mass is (approximately) evenly distributed throughout the wooden block then the mass will also reduce to a half of its original value and the density will not change.