For part a:
Archimedes' principle states that the buoyancy force acting on an immersed object is equal to the weight of the fluid displaced. Because half of W displaces the water, the force must also equal half of W.
So the answer is c] (1/2) ×W.
For part b:
For an object to float entirely above water, the density of that object has to be greater or equal to the density of the water (1.00 g/cm³). So for half of it to lie below the waterline, it must be half as dense (0.5 g/cm³).
So the answer is e] 0.5 g/cm³.
Hope this helps!
